Central European University Department of Economics
Central European University Department of Economics
PH.D. DISSERTATION
“CONTRIBUTRON”: AN INTERDISCIPLINARY STUDY AND AN AGENT-BASED MODELING TOOL OF HUMAN COOPERATION
By Szalay Miklós
Supervisors: Ugo Pagano (CEU) and Edmund Chattoe (Oxford)
May, 2006 Abstract
Cooperation is one of the most basic defining features of Human Society. It pervades all levels of human activity from families to international cooperation and constitutes the basis of any economic system. Right because it is a so central to social existence, many different disciplines embarked on exploring it with their respective scientific stances and methodologies. Moreover, although seemingly different, the various appearances of the cooperation theme contain certain common elements that can be abstracted and modeled independently. This dissertation is devoted to investigate human economic cooperation in an interdisciplinary manner and to model it as an abstract phenomenon. While the discussion in the first part focuses mainly at the individual level, with certain restrictions the modeling tool developed herein could be applied to capture cooperation amongst higher level units as well. Cooperation is complex. The nature of the mechanisms determining the behavior of the cooperating persons, the quality of the connections linking them together and societal institutions like social norms and the law all have fundamental effects on the emerging characteristics of large scale cooperation. Accordingly, to be able to look at the problem from a perspective and to gain a better understanding of the most general features of it, disciplinary boundaries must be traversed. The first half of this work is an attempt at conducting a thorough research aimed at compiling the most important findings of different fields concerning cooperating humans and human cooperation. The relevant areas of Economics, Psychology, Sociology and Law are covered, followed by an introduction into techniques that allow for constructing a formal model of such complexity: Agent-Based Modeling and Object-Oriented Programming. The second half of the dissertation develops a flexible computer simulation tool on the knowledge gathered in the first half, and applies it to a wide range of socio-economic situations and problems. It is not simply a model, but a versatile tool that allows the experimenter to impose and mix together a wide range of assumptions on the cooperating population and the structure of their interaction, to extract various data and statistics, dynamic and static, describing the agents’ behavior and its evolution, and to compare different scenarios quickly and efficiently. With parameters and initial conditions adjustable individually for all agents and the network structure freely variable it can handle complex situations inaccessible for analytic methods. Moreover, complete with a programmable front-end, it is an instrument that creates a possibility for experimentation, highly problematic in real-world settings. It is also capable to suggest new directions for experimental research.
- 2 - Acknowledgements
I would like to thank the following persons:
My parents, without whom I would be nowhere – in more than one sense;
My supervisors, Ugo Pagano (CEU) and Edmund Chattoe (Oxford) for their support and encouragement with the making of this dissertation and beyond;
My friends in Hungary and all around the world, for inspiring me and for keeping the faith in me;
The founders and the staff of the Central European University for all the opportunities these years gave me.
- 3 - Statement
Hereby I testify that this thesis contains no material accepted for any other degree in any other institution and that it contains no material previously written and/or published by another person, except where appropriate acknowledgment is made.
______Szalay Miklós
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0. Introduction...... - 8 - 1. Part I ...... - 15 - 1.1. Economic Foundations...... - 16 - 1.1.1. The Neoclassical Paradigm ...... - 16 - 1.1.1.1. The Fundamental Theorems of Welfare Economics...... - 18 - 1.1.1.2. Social Connections in Neoclassical Economics...... - 19 - 1.1.1.3. Economics of Crime...... - 21 - 1.1.1.4. Criticism...... - 23 - 1.1.2. Information Economics, Transaction Costs ...... - 24 - 1.1.3. Strategic Interaction ...... - 25 - 1.1.4. Experimental Economics...... - 27 - 1.1.4.1. Experimental Methodology...... - 27 - 1.1.4.2. Punishment and Contribution in Experimental Economics ...... - 28 - 1.1.5. Behavioral Economics...... - 32 - 1.1.5.1. Behavioral Concepts to Explain Pro-Social Behavior ...... - 33 - 1.1.5.2. The Evolutionary Methodology ...... - 35 - 1.1.5.3. Evolutionary Game Theory...... - 36 - 1.1.5.4. Evolution of Institutions...... - 37 - 1.2. Psychological concepts ...... - 39 - 1.2.1. Individual Traits ...... - 40 - 1.2.2. Social Psychology ...... - 41 - 1.3. Sociological Concepts...... - 43 - 1.3.1. Social Networks ...... - 44 - 1.3.2. Social Norms...... - 46 - 1.3.2.1. Social Norms in Economics ...... - 46 - 1.3.2.2. Definition of Social Norms ...... - 47 - 1.3.2.3. Classification of Social Norms...... - 49 - 1.3.2.4. Examples: Norms of Cooperatrion and Enforcement ...... - 50 - 1.3.2.5. Role of Social Norms ...... - 51 - 1.3.2.6. Enforcement of Social Norms...... - 53 - 1.3.2.7. Change of Social Norms ...... - 54 - 1.3.2.8. Limitations of Norms ...... - 59 - 1.3.2.9. Institutions of Enforcement...... - 59 - 1.4. Legal Outlook...... - 60 - 1.5. Interdependence of Norm Systems ...... - 62 - 1.6. Methodology ...... - 66 - 1.6.1. Agent-Based Modeling ...... - 66 - 1.6.2. Object-Oriented Programming...... - 69 - 1.7. Summary ...... - 70 - 1.7.1. Roadmap...... - 70 - 1.7.2. Lessons...... - 71 - 1.7.2.1. Multiplicity of Behavioral Patterns...... - 71 - 1.7.2.2. Free-riding – Central and Local Enforcement...... - 72 - 1.7.2.3. Adaptation and Networks...... - 72 - 1.7.2.4. Evolution of Behavior ...... - 73 - 1.7.2.5. Simulations and Experiments...... - 74 - 1.7.3. The Way Ahead...... - 74 - 2. Part II...... - 76 - 2.1. Related Models...... - 77 -
- 5 - 2.2. The Contributron©...... - 79 - 2.2.1. Hallmarks ...... - 79 - 2.2.2. Formal Description...... - 81 - 2.2.2.1. Implementation...... - 82 - 2.2.2.2. Agents...... - 82 - 2.2.2.3. Parameters ...... - 82 - 2.2.2.4. Exports ...... - 91 - 2.2.2.5. Network Types ...... - 91 - 2.2.2.6. Initial Conditions...... - 92 - 2.2.2.7. Agent Shuffling...... - 92 - 2.2.2.8. Initialization ...... - 93 - 2.2.2.9. Simulation ...... - 93 - 2.3. Discussion ...... - 94 - 3. Part III...... - 101 - 3.1. Analytical Findings ...... - 102 - 3.1.1. Behavioral Weighing and Utility-Based Maximization...... - 103 - 3.1.2. Connectivity of Networks ...... - 103 - 3.1.3. Compensating for Sight Range ...... - 107 - 3.2. Rational Updating ...... - 109 - 3.2.1. Central Punishment ...... - 109 - 3.2.2. Peer Punishment...... - 110 - 3.2.2.1. Discrete Case...... - 110 - 3.2.2.2. Continuous Case...... - 112 - 3.2.3. Distribution of Neighbors...... - 113 - 3.2.4. Summary of Findings...... - 114 - 3.3. Imitative transmission ...... - 115 - 3.3.1. Emergence of Optimum ...... - 115 - 3.3.2. Determinants of Convergence...... - 116 - 3.3.2.1. Network Structure ...... - 116 - 3.3.2.2. The Discount Factor, Noise and Certainty of Punishment...... - 117 - 3.3.3. Payoff and Average-Biased Imitation...... - 121 - 3.3.4. Summary of Findings...... - 122 - 3.4. Direct Effects...... - 122 - 3.4.1. Basic Features ...... - 123 - 3.4.2. Norm Cascades...... - 124 - 3.4.2.1. The Ignition Level...... - 125 - 3.4.2.2. Breakdown of Coopearation...... - 128 - 3.4.3. Oscillations...... - 130 - 3.4.3.1. The Basic Mechanism ...... - 130 - 3.4.3.2. Conditions of Oscillation ...... - 132 - 3.4.3.3. The Supportive Boldness Level ...... - 134 - 3.4.3.4. Continuous Oscillation...... - 135 - 3.4.3.5. Other Modes of Oscillations ...... - 137 - 3.4.4. Summary of Findings...... - 140 - 3.5. Heterogeneous Populations, Network Variations ...... - 142 - 3.5.1. Maximizers...... - 143 - 3.5.1.1. Maximizers and Average-Biased Imitators...... - 143 - 3.5.1.2. Maximizers and Payoff-Biased Imitators...... - 145 - 3.5.1.3. Imitation and Sight Range...... - 146 - 3.5.1.4. Detour: Perils of Network Effects...... - 146 -
- 6 - 3.5.2. Punishers ...... - 149 - 3.5.2.1. Punishers and Maximizers ...... - 149 - 3.5.2.2. Punishers and Payoff-Biased Imitators ...... - 150 - 3.5.2.3. Punishers and the Direct Effect...... - 152 - 3.5.2.4. Punishers with Variable Watchfulness...... - 153 - 3.5.3. A Mixture of Average and Payoff-Biased Imitators ...... - 155 - 3.5.4. Isolated Sub-Networks ...... - 155 - 3.5.5. Summary of Findings...... - 156 - 3.6. Policy Issues...... - 157 - 3.6.1. Policy Parameters...... - 158 - 3.6.2. Policy Statistics ...... - 158 - 3.6.3. Laffer Curves...... - 159 - 3.6.4. Policy Making with Severity and Certainty ...... - 161 - 3.6.4.1. The Classical Setup ...... - 161 - 3.6.4.2. Static Peer Penalty...... - 164 - 3.6.4.3. Dynamic Peer Penalty ...... - 165 - 3.6.5. Policy-Making with Imitators ...... - 167 - 3.6.6. Individual Maximization and Payoff-Biased Imitation...... - 169 - 3.6.7. Summary of Findings...... - 170 - 3.6.8. Further Possibilities...... - 171 - 3.7. Experimental Connection...... - 171 - 3.7.1. Calibration...... - 172 - 3.7.1.1. Estimating BUR ...... - 173 - 3.7.1.2. Estimating BUS...... - 174 - 3.7.1.3. Estimating BUDP...... - 175 - 3.7.1.4. Estimating PPE...... - 176 - 3.7.1.5. Determining Further Parameters ...... - 177 - 3.7.1.6. Weaving the Net...... - 177 - 3.7.1.7. Comparing the Output...... - 178 - 3.7.1.8. Acquiring Population Proportions...... - 178 - 3.7.2. Group Size Effect...... - 179 - 3.7.2.1. Reshuffling...... - 180 - 3.7.2.2. Group Size Effect on FULL and RING Networks...... - 181 - 3.7.2.3. Convergence in Watchfulness...... - 182 - 3.7.3. Certainty and Severity of Peer Punishment...... - 183 - 3.7.3.1. Mapping Parameter Combinations...... - 183 - 3.7.3.2. Finding the Optimal Mix...... - 186 - 3.7.4. Summary of Findings...... - 186 - 4. Part IV ...... - 188 - 4.1. Validity...... - 189 - 4.2. Achivements...... - 189 - 4.3. Further Research ...... - 190 - 4.4. Future Development...... - 191 - 4.4.1. Agent Properties...... - 192 - 4.4.2. Network Extensions ...... - 193 - 4.4.3. Miscellaneous Improvements...... - 193 - 5. Appendix 1 – Parameter Arrangements and Abbreviations...... - 195 - 6. References ...... - 198 -
- 7 - Introduction
We are living in a world of scarcity. And “we” does not only stand for humans. Everything that is alive lives because innumerable generations of its predecessors governed by the various forces of selection successfully adapted to the ever changing conditions of scarcity. This process, by definition, strongly selects against everything that do not bear the commandment “survive” carved thoroughly into every little part of its assembly. For survival adaptation is necessary, for adaptation selection is necessary, for selection reproduction is necessary and for reproduction certain resources are necessary − and resources are limited. It is written into the fundaments of our very existence that we have to compete for them if we want to fulfill life’s eternal commands: survive and multiply. There is, however, more than one way of competition. We can compete against the whole world on our own or we can join forces with other beings in the same situation. Cooperation has its advantages and disadvantages. The two most important advantages are economics of scale and specialization. The first by fusing contributions culminates in achievements from which all can benefit but which no one of the contributors could get on its own – in economic terms to purchase public goods. The second by providing protection from the community allows for more efficient ways of carrying out tasks to emerge.1 At the same time, working together requires coordination, which is not for free, and this is a reason why more sophisticated systems after a point tend to become more fragile.2 Nevertheless, teaming up is story of success: commenced by cells sticking together to build plants and animals, up to modern human societies, communities have stood a firm chance in competition. But being a member of a community always requires subordinating individual interests to the needs of the community. While we are talking about cells, plants and social animals this is not really a problem as they can be programmed to sacrifice even their lives. Their program can fail and sometimes it does, bringing about mutations that attempt to free ride. This is when we are talking about cancer, for example.3 But this is only blind error – although there is always a pressure towards the emergence of free-riders by definition, what is lacking is conscious opportunism. We encounter a qualitatively different problem when individuals become capable of recognizing that there is a possibility for free riding on the community whose productive members they are supposed to be. It happens when the components grow to be conscious. It happens when we approach humanity.4
1 Examples for public good at the biological level include memory and consciousness, and at the societal level national defense, roads, etc… Examples for specialization at the biological level are the different specialized cells and tissues of an organism, and at the societal level the different professions and industries. 2 Note that in a group the number of possible connections between members grows much faster than that of the elements. 3 Some would call viruses and other parasites free riders, too, but in the sense we use the word here this is not correct: these creatures are not supposed to co-operate with the host ab ovo. 4 (1) A machine (say a cell) can be repaired or replaced when it malfunctions and turned back completely into its “cooperative state”. On the contrary, people once they recognize the advantages of opportunism will hardly forget about it. Moreover, they probably also have an idea about the means they could use to exploit the opportunity. (2) Macy M.W. (1998) (Quoted by Caldas and Coelho (1999)) notes that nature played “a cruel trick on our species: we cannot survive alone, yet unlike social insects we are not genetically hardwired for co-operation.” This is a price that we pay for our rationality. But I would like to add that it is not true that we do not have genetic background for co-operation, even among the non-kin. Firstly we have the differences between the sexes: we need to co-operate for a successful life. Another sign is the variability of talents in the population, or at least the flexibility of our minds that allows for specialization into different professions. Thirdly, we have our genetically provided ability for language, which on the one hand must have emerged through the co-evolution of
- 8 - There are countless situations in human society when free-riding is a potential problem: starting from verbatim free-riding and continuing through phenomena like waiting for flat mates to do the washing up, shirking in team work, breaching cartel agreements, excessive usage of non-excludable common resources with rivalry and avoidance of tax payment, one could list the various manifestations endlessly. More recently, we have evidence from controlled economic experiments, too, on various aspect of the problem. Naturally, all of these facets have their individual characteristics, but there are at least three things common to all: firstly, subjects are humans with characteristic sets of possible motivations and behavioral patterns; secondly, these individuals are associated and connected to each other in situations when they have to sacrifice something for the common good and consequently have an incentive and many times opportunity to free-ride; and thirdly, the community needs to have means to enforce pro-social behavior. Nevertheless, most of the time people seem to behave in line with social expectations without apparent enforcement taking place. A few words are appropriate here about how I see the structure of the mind, the mental foundations of human behavior.5 I think that in the mind of human beings there basically two levels: an underlying “personality” and a superimposed “consciousness”. The personality is formed partly by the genetic heritage, partly by early experiences in life and it is constant or at least changes very sluggishly later in life. On the other hand the content of the conscious self is built up mainly by education and cultural influences, and is much more flexible and prone to external influences. These two levels are in perpetual interplay, moreover they are often in conflict and the apparent behavior of the individual emerges from this ongoing interaction. How does this mental model relate to our topic – pro-sociality and free riding? In my view people can be different at both levels. There are people who are “good” by personality. In this case there is no need for enforcement whatsoever.6 Next, there are those who are flawed by personality, but who at the same time want to be good on the conscious level. This is what I call internalized enforcement. There are two subtypes here: firstly there are those who have an internal definition of goodness to relate themselves to – in other words those who have conscience. Secondly there are people who measure themselves by external definitions and norm systems: ethics, social norms, religious rules and the law, and who see goodness as a measure of compatibility with these rules. Finally, there are those who are flawed by personality and who are opportunistic at the conscious level as well. This is the situation when society must fall back to external enforcement to keep them behave pro- socially. Enforcement can be achieved in a variety of ways. First of all I make a distinction between various means and channels of enforcement. By means I understand the different ways of how enforcement is implemented in society that is the different social institutions of enforcement. By channels I mean the different features of human beings through which their social and biological features, and which on the other hand has only a use if we are to co-operate with other people. 5 This is admittedly a subjective and simplified picture which does not necessarily correspond to any established school or paradigm, but I think it is a clear cut working hypothesis. 6 (1) People are likely to be equipped with some kind of natural tendency to restrict defection in communities. The possibility of a genetic inclination to pro-sociality and to punish free riders can come from that there has been a sufficiently long time since the awakening of the selfish mind for biological forces to affect our physiology – through group selection for example. Moreover, cultural transmission in the family is also a major factor establishing pro-sociality at the level of personality. (2) In spite of the fundamental pro-sociality of this type the conscious mind can still adversely interfere with the underlying personality. This is the case when intentions are good, but due to erroneous ideas on the definition of good, on reality or on the applicable means to achieve it the outcome does not match the intentions.
- 9 - behavior can be affected. Means can be classified in many ways, for the present work the most important division being between informal (organic, spontaneous and mostly distributed) and formal (planned, institutionalized and mostly centralized) means. On the one hand there is a wide range of informal traditions and social norms directing individual action for the benefit of the community. On the other hand societies and smaller communities also established formal institutions firstly to organize human interaction and secondly to inspect the behavior of their members and chastise dangerous deviations. Besides, people informally or institutions more formally can conduct their influence through many channels. We can rely on psychological instincts and impulses: conditioning used to be seen as the main mechanism molding human behavior and it still holds important positions. Secondly, we may try to utilize conformism and imitation, phenomena widely recognized in Sociology and Psychology. Thirdly, we can appeal to rationality, once the sole motive of Homo Economicus. In real societies all this variety of means and channels of enforcement work simultaneously in influencing human behavior. At the same time they are very likely to affect the same person differently in different situations: firstly because we are exposed to them differently in different circumstances and secondly because people themselves may change. Conversely, because people are different, these influences have different bearing on different people even in the same situation. Furthermore, as people live connected to each other, some influences are transmitted in a social network to further complicate understanding. Until scientist were willing to abandon much of the above complexity for predicting or explaining behavior in general, or for the better case just restricted themselves to the exploration of cases when one or another force was overwhelmingly potent, it was possible to create clear-cut theories, use simple tools and come up with elegant analytic solutions. These theories are not without use, because there really are conditions when they match close enough with reality. But if we want to get closer to many real-life phenomena we should not be deterred from considering more complex situations. This requires an interdisciplinary approach and to handle our findings in a formalized manner we also have an excellent instrument in our hands: social simulation. This dissertation has a twofold objective. Firstly it intends to compile the most widely acknowledged theories and empirical findings concerning the cooperation – free-riding phenomena and the associated patterns of human behavior from across the social sciences. Secondly, building upon these fundaments it aims at developing a flexible social simulation tool that can be used to compare the outcome of a wide range of assumptions on cooperating communities facing a free-rider problem, and which is capable to contribute to answering many important socio-economic problems associated with collaboration. The model described in this dissertation has been built up directly from basic theories. It had to be so, because, to my knowledge, it is the first agent based tool created to model contribution and punishment with such a comprehensive range of behavioral patterns and detailed parameterization – and also because it is an inherent property of agent-based models that they capture their subjects through a natural description – that is by their basic features. “Contributron”7, so goes the name of the tool, is a sequel to “Taxomaton” an agent-based model in the same topic also designed by me. Taxomaton was more of a “conventional” model of limited horizons, aimed at the exploration of a system with several specific assumptions on agents and social structure hard wired into the code. It delivered interesting results, though, concerning the certainty-severity problem (which we will soon encounter), the
7 “Contributron” is a newly created word. It suggests that the tool developed herein is an electronic automaton designed to model people’s contribution to common goals.
- 10 - comparison of central and local punishment, and a couple of others, too. Nevertheless, I have realized two drawbacks: one, that there were many implicit underlying assumptions that other scholars may see otherwise, and two that it lagged far behind the level of realism that agent- based models allow. This is why I decided to create this new model on the legacy of Taxomaton. At this point I had two choices. I could have again imposed my assumptions on the model, by fixating the additional mechanisms and parameters to the values thought best by me, or let them freely variable so that others can also possibly fill in them by their best knowledge, and observe how the results relate. I decided for the second option, because it was a new and promising approach with farther looking potentials. Thus, I must emphasize that Contributron is not a simple model, but a modeling tool that lets experimenters quickly assess and compare the consequences of different assumptions on human behavior and social and institutional context. It has been designed to include the most widely acknowledged behavioral patterns, many of them already modeled separately, but – as far as I know − never put together to such extent. However it must be underlined that the model actually simulated does not necessarily involve all of the elements that the tool is capable to handle. The choice of which elements to include is left to the experimenter, who by varying these elements is capable to compare many different situations quickly. Another pivotal characteristic of the model is the width of the range of exported data that allows for tracking every aspect of the underlying dynamics. The basic idea of Contributron is achieving maximal flexibility in assumptions as well as in the addressable questions, leaving the opportunity of choice to the experimenter in both aspects. Also for this reason it is impossible to give an exploration of the parameter space anything close to completeness herein. The most useful thing I can accomplish is to highlight the most important principles for modeling and demonstrate the model’s functionality and power with a number of carefully chosen examples. I would like to bring up two somewhat philosophical ideas connected to the design of my model. The first concerns how we approach modeling in general. Most models until now have clearly been associable to one or another discipline or rather paradigm, relying practically exclusively on its methodology, postulations and theorems. We must understand, however, that deeper models are not necessarily better than wider ones. It depends on the aims to be achieved. Deeper can be better when the modeled phenomenon is very special. But in real social life there is no warranty that certain problems are sealed from each other, especially because it is the same being who should act so differently according to the distinct disciplines. This is why while deep models can be extremely meticulous from some aspect, they are liable to miss fundamental points from another. Moreover, if a phenomenon has general characteristics, and the contribution-punishment puzzle clearly has, until we approached it in a more abstract way we effectively renounce induction that could subsequently greatly facilitate obtaining special knowledge. The second idea is that in social sciences when we deal with special models that are mute about things beyond the frontiers of their respective fields, it is not true that they do not take a stand on issues belonging to other areas. There is always an implicit decision about all potential phenomena that might play a part in the situation in question, even if it is not expressed. It is written in the axioms of the corresponding paradigms, which quite often contradict with their concurrent counterparts. An important characteristic of my model is that here we have to be a little bit more explicit. Let me summarize what my model is intended to achieve and what is beyond its scope.
Goals:
- 11 - ● Supply qualitative results to formulate hypotheses in connection with (including but not limited to) the consequences of different behavioral patterns and network structures, population heterogeneity, policy issues and experimental setups ● Facilitate the assessment and comparison of the consequences of special assumptions on agents / social context / institutions, across different paradigms and different manifestations of the general contribution problem. ● Suggest new directions for Experimental Economics ● Inspire the creation of specialized models for special manifestations of the contribution – free-riding – punishment phenomena, and provide a framework that can be modified or extended in the future ● Serve as a research tool – and as an example for building similar tools beyond the scope of the present dissertation – both in the substantial and technical sense8
Limitations: ● Although it can be easily brought much closer to realism than the bulk of the analytical work so far,9 it is not claimed to be able to exactly mimic any special form of the contribution phenomena. This is a general model of a general problem, while special problems require special models. ● Contributron is not claimed to be perfect. We will see that there are already much more behavioral regularities identified by various disciplines than those finally included into the model. Even though the range of the phenomena integrated is much broader than traditional models, I also had to draw a borderline between more and less important, party because the extent of the present work, partly to keep the model transparent and tractable. Nevertheless, I am going to recommend several ways of extension and perfecting in the final part.
Agent based models seize basic features of the agents. In our case, we find that the factors influencing contribution and punishment behavior are rooted in divided grounds separated by disciplinary boundaries. Before I could start to work out the model, I recognized that first I needed to accomplish a survey of several fields to gather the most important results and theorems concerning human behavior in relevant situations. The most compelling reason why I had to go down to the primary sources was that I could not find a comprehensive work that summarized the knowledge that was needed to realize this project. This is how collecting the first-hand information of these distinct subjects at least to the extent that makes the creation of my interdisciplinary model possible became the first objectives of my work. I have tried to extract the most essential findings of these fields for building a model that faithfully reflects an image of cooperating man the closest possible I could get to reality. This literature review includes the relevant areas of Economics, Sociology, Psychology and Law with an outlook into Agent-Based modeling techniques and Object-Oriented Programming. There are several of my notes added and it is complete with highlights on the most important conjunctions between the various fields. The nature of the problem at hand can probably account for the length and special approach of this run-up to the actual model
8 In addition, the Mathematica front end – which essentially deals with controlling the simulation part, data handling, analysis and visualization – could be easily modified to accommodate completely different projects. 9 Of course due to the difference between the methodologies results are less stringent, too.
- 12 - description. I hope that this survey in itself will be able contribute to the attainment of a more realistic behavioral picture of man. Naturally, there is no room in a dissertation to gather up everything that is connected to such a general problem, which is why I needed to select certain areas to focus at and restrict myself for only briefly mentioning other related issues with giving appropriate references. However, the reader should note that in order to build a model with such a wide range of capabilities there is a need for getting an encompassing view on the problem, there is a need for gathering the most valuable findings of the different disciplines and paradigms that usually are isolated from each other. This has also been brought about by the methodological shift we observe: agent-based methods allow for a substantially higher degree of complexity than the analytical approach, and I felt that the limits by today are far off from the models built up to date. On the other hand by linking the findings of different disciplines there is an opportunity to find synergies so far concealed by the walls that fragmented our realm of knowledge of the world.10 The interdisciplinary study makes up the first part of the dissertation: we go through the respective disciplines one by one laying special emphasis on Economics and Sociology and leaving the methodological essentials to the end. The second part first lists the models from the literature most closely related to Contributron, next my model is described, and subsequently a few elements are discussed in the light of our findings in the first part. The third part is devoted to demonstrating the model in action. It consists of seven chapters. The first presents some analytical results useful for connecting behavioral rules to utility maximization, for understanding model output in subsequent chapters, and for the correct application of the model. The following three chapters concentrate on the three main behavioral regimes built into the model, maximization, imitation and direct effects, singled out so as we are able to study some typical phenomena closely associated with them. The final three chapters in this part turn to typical applications of the model, each of them focusing on a different set of problems from the behavior of heterogeneous populations through policy questions to the connection between real-life experiments and simulations. It is important to call attention to that the application part has been designed with many purposes in mind, described in detail the third part. The fourth and final part concludes and recommends directions for further research and development. A more elaborate roadmap is given at the beginning of each part and chapter. A final remark is necessary before moving into the substance. The reader will realize shortly that the present work is structured slightly differently from the standard. The reason is that the motivation behind it comes from two directions: on the one hand the realization of the common elements and key differences between the special manifestations of the general contribution – free-riding – punishment phenomena, and on the other hand the recognition of the variety of ways through which the different branches of social science approach the same problem. These two motivations were subsequently completed with the understanding of the opportunity for synthesis using our new modeling techniques. I must emphasize as early as now that the special questions analyzed in Part III are only examples selected to serve a number of aims set down in detail in the beginning of that part, and they do not add up to the direct reason why the model was built and why this dissertation was written.11 It is understood
10 In my view we, also as scientists, are interested in the World – not Economics, Sociology, Psychology, etc… – which categories have been created only for facilitating the practical work of research. I do not claim that the reductionist approach does not have its merits, but I am positive that the final aim in front of us is a unified, holistic understanding of the phenomena around (and inside) us, however idealistic it may sound. 11 This is also the reason why this dissertation does not harbor a big central hypothesis. This work is basically a methodological one creating a new tool, rather than concentrating on a very special question to be answered. (Similarly to when one creates a new estimator in Econometrics. Contributron, though, by the characteristics of
- 13 - that one could write lengthy books should he intend to give a complete examination of those questions even in the framework of Contribution for there are so many combinations that the model allows for. Accordingly, the central aim of the dissertation is the exploration of the different branches of social science, gathering their most valuable ideas and findings concerning human cooperation, and the integration of this knowledge into a flexible tool that is capable to compare the consequences of many different assumptions regarding human cooperation and to convey intuition and deliver results for many different socio-economic questions – hopefully even beyond the scope of this dissertation. Contributron is handed over to the community of social scientists for consideration.
the technique, is more qualitative but at the same time much more versatile as well.) It must be added, however, that there are many interesting distinct results concerning typical socio-economic problems in Part III.
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1.Part I
An Interdisciplinary Study of Human Cooperation
- 15 - This part provides the background for my model by giving an overview of different disciplines and their most momentous findings concerning the problem of human cooperation. In connection with Economics I spend some time discussing the development of the image of economic man and human cooperation because it is indispensable for us to be able to put the present project into context and take the next step. Experimental and Behavioral Economics, however, get special attention, because these are the areas that opened up the road for interdisciplinarity and a brave new Homo Economicus. The following chapter is a shorter interlude on individual and social Psychology, indispensable because behind the behavior there is always the mind, and without at least a basic understanding of it any attempt to build a valid behavioral model is doomed. It is followed by a lengthier excursion into Sociology, with special emphasis on social networks and social norms, basic elements of human interaction (and also my model). The rationale for this is that what we are really interested in is many times the large scale consequences of local interaction – and also that Economics has paid far too little attention to social norms up to now. A short legal review follows for demonstrating how the archetypal central institution of enforcement works for securing pro-sociality, and to get an insight into the interdependence of norm-systems. Finally, before embarking on the model design and implementation we have to tell a couple of words about methodological questions including agent-based modeling and object oriented programming. Important connections are highlighted and some remarks added at various points.
1.1. Economic Foundations
This chapter presents the relevant development of the image of economic man, a process that starts with a crystal clear model of perfect selfish rationality and ends up on an interdisciplinary frontier zone. Meanwhile important concepts are defined and put into a new light allowed by hindsight. We start out with a short introduction to the Neoclassical Paradigm. Externalities and public goods are introduced as the first signs of social embeddedness of economic activity. Next we get an insight into the Economics of Crime to understand how pro-sociality and defection is seen from the neoclassical point of view. Then we consider the steps through which the extremely simplistic orthodox model began its journey towards acknowledging that people are more (and less) than stone cold and perfect calculators. After presenting the most important ways the neoclassical paradigm is criticized we consider the dimensions of departures and say a couple of words about Transaction Cost Economics and Economics of Information. In turn we arrive at strategic interaction and Game Theory, important milestones on the road to our contemporary understanding of human interaction. Then we are going to learn about the most important experimental findings supporting the need for better models, followed by a summation of novel ideas relevant to our agenda in Behavioral Economics.
1.1.1. The Neoclassical Paradigm
The Neoclassical Paradigm is the first fully developed system that predicts spontaneous order emerging in the economy stemming in decentralized interaction.12 It is indispensable to touch on it because the problems we are struggling with are still much the same that orthodox scholars addressed in their own way and the limitations of this system is
12 Bowles (2003) is an excellent source of information on the development of Economics departing from the Neoclassical Paradigm. It is the primary reference for this chapter.
- 16 - what motivates current research, including mine. This brief summary of the most important elements of the Neoclassical Framework serves multiple ends. Firstly, it tells us about the baseline view of Economics on human beings and the structure of their economic relations, the starting point in a modern quest for a better description of economic actors. We are going to see the main restrictions imposed on this image of man (the original Homo Economicus) and their system of interaction (the Neoclassical market), which at the same time mark the points of attack for possible departures − like mine. It also provides us with a picture that can later be contrasted with the gradually unfolding image I attempt to paint traveling through the domain of several disciplines. In turn, we are going to see the most important results that the Neoclassical model could deliver − and also the boundaries where it had to stop. Again, the reason for it is neither that I believe in the validity of these findings nor that I need them constructing the model. My aim with it is on the one hand to show what kind of results could be obtained by the old ways, so that we have a solid object to relate to when considering what is possible along our new lines − and on the other hand to sketch up some of the sub-surface shortcomings and the questions that has been left without an appropriate answer. Secondly, this section highlights the difference in methodological questions between the analytic treatment allowed by simple assumptions and the experimental approach necessitated by complex problems. Thirdly, it is a good way to elucidate the meaning of some old notions, externalities and public goods in the first place, that required special attention from the old theory already, and which appear in a new light when we restate our problems in a social setting. Fourthly, we cannot start finding new solutions to a problem − pro-social behavior − without first checking out how older theorems attempted to answer it, and how they failed to come up with viable propositions. This is what our review of Economics of Crime is devoted to. Fifthly, our kick-off will help us to see the reason why I have to save rationality as one of the key elements of my model. Although the Neoclassical view has been criticized vehemently for its bias towards human rationality, we would commit the same mistake again if we bound ourselves to a different mechanism without acknowledging that the original Homo Economicus bore an essential element of real mentality in himself. We have to keep in mind the traditional methods and results of the analysis of human cooperation in order to be able to take a step further. The Paradigm has two defining tenets. Both of them are central for obtaining its famous results. One of them concerns with the economic actors − either people or firms, the other the interaction between these actors. They constitute an extremely abstract view of the interacting entities and the economy itself in order to attain mathematical tractability and clear-cut predictions. The most important feature of the economic man of the Paradigm, the archetypical Homo Economicus, is of course his self-interest. This is the only motive that governs his actions: he does everything to maximize his own utility, given by exogenous and fixed preferences. (Convexity is also usually supposed.) He has perfect knowledge of all relevant information in the economy while information processing is costless and perfect for him: all decisions are taken based on far-sighted evaluation. Because he is already perfect he does not need learning, there is no role for experience or evolution. Neoclassical firms function in much the same way. They are self-contained entities with the same perfection of selfishness, foresight and analytical ability as individuals. However, they populate the supply side of the economy being the producers of the products sold on the market. Production is achieved by a well-defined production function, which determines how inputs can be turned into products, and how products can be transformed into each other. Selling them firms face a demand function on the market that seamlessly determines the relationship between prices and quantities. Non-increasing returns to scale are
- 17 - generally assumed to secure existence and uniqueness of equilibrium. Firms are also maximizers: they seek to achieve the maximal profit that is available for them. The structure and operation of the economy is equally smooth. Its central feature, the second crucial assumption of Neoclassical Economics, is complete and costless contracting. This involves that obligations of the parties are completely determined ax ante, that there are no search or contracting costs. Enforcement of the terms is also free, undertaken by third parties that is courts. Therefore, there is no room for monitoring or informational problems: opportunism is precluded both for individuals and organizations. Actors are connected to each other solely through these contracts: there are no other kinds of social interaction or moral obligations; all relevant information about other’s actions is mediated by market clearing prices. Markets are ‘The’ institution of economic interaction, where contracting takes place. They are given exogenously: their evolution and that of prices themselves are mostly ignored. But the market is not only a place where contracts are made. It also mediates prices revealing all the relevant information about preferences and production possibilities that is necessary for individual maximization and decisions. Market contracting is the only way people of the orthodox Neoclassical society are connected and can affect each other. Consequently, if market rules are well designed, to the extent that makes exchange between the selfish minded actors efficient, there is no further need for personal virtues: “good rules displace good citizens”. This optimality is established by the Fundamental Theorems of Welfare Economics. The assumptions made by the Paradigm are very stringent, indeed. We will see that now it is clear that real people are subject to and their behavior is influenced by many other factors than narrowly defined self-interest − which in several situations cannot be ignored. The above restrictions, however, allowed the derivation of equally strong results concerning the efficiency of market exchange. Nevertheless, as Bowles notes13 even the authors of these theorems were clearly aware the unrealistic nature of their tenets.14 Notably Marshall, the earlier of the founding fathers of the paradigm, explicitly raised many issues that are subject to recent economic research, including increasing returns and non-selfish motives. These ideas, though, were completely expelled from mainstream theory: they did not fit into the rigorous Walrasian framework which paid no attention to many important societal and psychological phenomena. Nevertheless, nowadays these ideas are beginning to find their way back into economic research. We will address them in the following chapters but first let us take a look at the celebrated results of the old school.
1.1.1.1. The Fundamental Theorems of Welfare Economics
The Fundamental Theorems channel the postulates on selfish maximization and complete markets into an economy-wide optimal order of allocations, prices and outputs.15
13 Bowles (2003) Ch. 6. 14 Why these simplifications were so easily accepted has probably much to do with the fact that the theorems based on them provided market capitalism – the prevailing economic system in the western world – and its beneficiaries with very strong arguments and the authority of science for the “goodness” of the system and “rightfulness” the status quo. 15 The first of these theorems, as derived by Arrow and Debreu, states that assuming economic actors and contracts as above described: All equilibria resulting from an initial allocation through the mechanism of competitive exchange is Pareto optimal. The second theorem takes an additional assumption: convexity of preferences and production possibility sets. Basing on them it states that: Any Pareto optimal allocation can be achieved by some initial endowment and the subsequent competitive equilibrium.
- 18 - These statements are very strong. They assert that we need nothing else, but free markets and all possible efficiency gains will be exploited in the economy automatically.16 Markets on their own are capable to organize private action in a way that leads to the spontaneous emergence of an ideal social order. Note that as early as here we meet a large scale phenomenon resulting in from uncoordinated interaction17. Another noteworthy thing is that the economy-wide general equilibrium emerges from individual equilibria: we have a static equilibrium here, where not only the economy, the aggregate of actions, but all participants are in equilibrium simultaneously. In general, however, individual stability is not necessary for system-wide stability of dynamic systems.18 But if the world would be so simple, there would be much less need for painstaking efforts in practical Economics. The first clear problem with the Theorems is definitional. Pareto efficiency says nothing about equity, which – to some extent – is critical to every benevolent social welfare system. Thus, the theorems only assert that there is no way to make somebody’s utility higher without making somebody else’s lower. Neoclassical markets do not create a just outcome, however due to the second theorem any Pareto optimal outcome – including more just ones – are attainable through a wealth transfer followed by market exchange. Second, there is no answer for the question how the market clearing prices that are accepted by all actors come about, the dynamics of the system is ignored. Third, uniqueness of the equilibrium is not guaranteed. All these problems stem from inside the theory that is they have nothing to do with the postulates that lie in the heart of the theorems. They simply mark the frontier that deduction from the axioms can reach. Today the underlying assumptions are also subject to strong criticism because of their restrictive nature. We are going to see shortly how criticism got a foothold first trying to avoid to harm rationality, but first we should touch upon a couple of ideas that the Paradigm seemed to be able to treat within its own kingdom.
1.1.1.2. Social Connections in Neoclassical Economics
There are a number of phenomena in economy that markets clearly fall short to treat. The two most important are economic actions that affect third parties (externalities) and goods that must be consumed by everyone equally (public goods). These are the first ‘societal’ questions that Neoclassical Economics had to face and solve − they are the most prominent examples where spontaneous order of markets seemed to fail. They are still among the biggest problems communities must respond in spite the Paradigm seemed to managed to find a way to meet these challenges in its own style.19
1.1.1.2.1. Externalities
16 For a more complete analysis see e.g. Mas-Colell et al. (1995) p.305. 17 Although it is not local in the sense that here agents can freely interact with anyone in the same market. 18 An example for a stochastic market model showing large scale stability is Foley (1994) as cited in Bowles (2003), Ch. 6. Not to mention Physics where ‘averaging out’ is the fundamental way large scale stability is supported in many dynamical systems (e.g. gases). (Foley’s model has also been adapted from statistical mechanics.) Nevertheless, one should be careful with this idea, because exactly in those systems that we are primarily concerned with (a large number of locally interacting agents), simple averaging often does not work. More on this later. 19 Any Microeconomics textbook covers these topics extensively, e.g. Varian Ch. 32.
- 19 - When an action affects the wealth or utility of third parties that are not involved in the decisions about it an externality emerges.20 This is clearly different from market transactions as supposed by Neoclassical economists: actors affect each other via non-contractual means. However far it is seems to be from social norms and pressure, it is the first gap that opened the way for societal considerations. In fact it is probably the most persistent and encompassing problem that any group of people must cope with and it appears in various disguises. For instance our central theme the free-rider problem is also an externality problem: the free-rider inflicts a negative externality on the rest of the group. What changed since Neoclassical economists came up with their answer is first the definition of externalities, second the place where we look for the solution. Orthodox scholars found that externalities arise because of poorly defined property rights or lack of markets where these rights could be traded. We immediately see that the free-rider problem does not fit into this definition: to be a free-rider is definitely an offence that is property rights are well defined. Why is this controversy? The problem with free-riders is something else: enforcement, which of course in the Neoclassical framework is not a problem, therefore free-riders do not exists, therefore they do not cause externality. This is the way questioning old axioms leads to generalization of old notions. And of course redefined problems require reconsidered answers. But let us see first how the old Paradigm succeeded in answering the problem of its own definition of externalities. Externalities are a menace to the efficiency of markets because then demand for a good whose production costs are partly external does not correspond faithfully to the total social cost (or gain) it incurs, consequentially efficiency is lost. There are three basic kinds of solution for this problem. All of them aim to channel back the excess social cost onto the actor who caused it. The first is internalization. When all the assets involved are owned by one actor, the externality is eradicated and the problem is solved. The second solution is the Pigouvian taxation. The basic idea is that a central authority should levy a tax on the producer of the negative externality (or offer a subsidy to that of the positive externality) which should be equal to the emergent social cost. The problem with this solution is that the socially optimal level should be known by the state ex ante, which could be only possible by knowing all the preferences of the actors. The third idea is the so-called Coase Theorem. It states that even when externalities are present, as long as agents are able to bargain over the rights that give rise to the actions that result in the externality, the socially efficient level can be attained. All is needed are well defined property rights that makes efficient trade over the externality possible. Critics, however, note that if bargaining over property rights are obstructed it is likely that trade about rights on externalities will also be. What is common to all these propositions is firstly that the underlying assumptions are the same as for the Fundamental Theorems except for one: extra-contractual effects are present. On the other hand the assistance of a central authority seems to be inevitable21 either to define and defend the property rights by providing costless enforcement or to impose the appropriate tax. When later we are willing to relax more restrictions, new opportunities come about for externalities to emerge requiring new means of solution: what we will face is not lack of markets or indefinite property rights, but a public good problem.
1.1.1.2.2. Public Goods
20 The most popular examples are environmental pollution, and the famous “Tragedy of the Commons” (Hardin (1968)) (negative externalities) and bees collecting pollen from neighboring gardens while at the same time pollinating the plants (positive externality). 21 Solving societal problems by the state is of course an old idea. Recall e.g. Hobbes’ Leviathan.
- 20 -
The second well known example that gives rise to out-of-market interdependence is public goods. As a matter of fact the public good problem is again a special case of externalities. Here just like in the case of simple externalities the independent decision of each agent affects the utility others. However, now there are always more than two actors involved and the externality is always positive: consumption by an agent raises the consumption of all the others.22 The problem arises because contribution from an agent raises the quantity of the good only marginally which is why everybody has an incentive to undercontribute, resulting in free riding and an undersupply of the public good.23 This situation also appears in the contribution problem: (costly) enforcement is usually seen as a public good that should be purchased (carried out) by a community which is why Neoclassical tenets predict insufficient enforcement and a breakdown of cooperation. The proposed solutions are similar to those encountered with externalities: privatization to internalize the external effects or some kind of external regulation. The external regulator can be a (benevolent) social dictator who by attempts to aggregate the individual preferences into a social welfare function, then tries to find the socially optimal quantity by maximizing it, and finally forces the agents purchase and consume that amount. Unfortunately, it has been shown that it is not possible to construct a well-behaving non- dictatorial social welfare functional. 24 In addition, various voting schemes have been proposed in quest for a less dictatorial solution. None of them turned out to be perfect, because either agents have an incentive to distort their true preferences (majority rule) or aggregation is imperfect (median voting), or the solution is not Pareto optimal (Clarke Taxation). There seems to be no general solution for the public good problem even on Neoclassical grounds. Insisting on the Neoclassical assumptions, all proposed solutions to the public goods problem, and more generally to externalities neglect important societal and psychological phenomena. Today it is admitted by a swiftly increasing number of economists that norms, conventions and peer penalty have a strong influence on people. The image of economic man is also in transition: Homo Economicus is more malleable now, featuring endogenous and other regarding preferences. Equipped with our more realistic postulations we are able to discern new and promising solutions to old problems and market failures. Societal forces outside the vicinity of Economics for so long now have been shown to be capable to positively complement states and markets in organizing human interaction both by empirical and theoretical studies.25
1.1.1.3. Economics of Crime
Before leaving the Neoclassical theme behind, we need to get acquainted with the way the Neoclassical tenets was applied in theories on criminal deterrence and enforcement of pro- social behavior. The founder of the area is Gary Becker (1968).26 He used the traditional Homo Economicus to build a utilitarian image of the criminal, who in his world is just as
22 A usual example is national defence. 23 From a game theoretic point of view, this situation is also a variant of the n-person Prisoner’s Dilemma. 24 Well-behaving meaning that it aggregates individual preferences satisfying Pareto efficiency and independence of irrelevant alternatives. This result is known as Arrow’s Theorem. In more detail see e.g. Kreps (1990), Ch. 5. and Varian Ch. 35. 25 More on community governance in the summary of evolutionary economics. 26 A very clear introduction to the topic is Varian (2003) Ch. 32.
- 21 - much a rational actor as any consumer. The criminal, says Becker, when deciding whether to commit a crime simply tries to maximize his expected payoff, which is composed of the income generated by the crime minus the expected punishment: severity times certainty of the punishment. Hence, authorities have to decide on two factors: how much to invest in detection and how severe the punishment should be. As we will see this is an ongoing issue in other social sciences, too, each approaching the problem from its special direction. The most interested seems to be the legal academy, not surprisingly coming up with alternative treatments and solutions, about which we will learn more later. Nevertheless, given the distinctive stance of Neoclassical Economics the answer to this problem seems to be quite straightforward. Because increasing certainty of punishment is supposed to be costly, while making it more severe is not – conversely, fines even generate additional income for the state – the common policy recommendation is maximal severity with minimal certainty.27 However, many models consider that crime should incur an increasing marginal cost to prevent committing more serious crimes once someone is already liable. Then, having a suitable function determining this, using simple maximizing techniques the optimal level of detection can be obtained. Most models seek this fixed optimal level of detection28. There is another issue that does not emerge until Economics admits the existence of moral hazard. It is conceivable that an effective central enforcement system undermines civic willingness to participate in crime prevention. This does not necessarily have anything to do with social norms, it is enough that individuals become less vigilant and invest less than optimal into security, inflicting a larger burden on central authorities and deteriorating social efficiency. In these cases Economics usually recommends under-deterrence by law. The same method and its variants has also been applied for tax evasion, first proposed by Becker and taken forward by various authors. 29 The original approach uses fixed probabilities of detection similarly to the general case, and usually arrives at recommendations much like above: high fines and low probability of audit. (Again, because audit is supposed to be costly.) More recently multi-period game theoretic models have been devised that seek to answer various questions like how to minimize tax evasion, maximize revenue or social utility.30 Tax authorities, however, typically play a passive role: detection probability is generally fixed.31 Most models being analytical, social network interaction and more complex behavioral issues are outside of their analyses: they concentrate on creating optimal incentives for rational actors despite empirical works have shown the importance of societal factors.32 The basic picture is of course greatly oversimplified. Crime in the neoclassical framework is just another good with a price, the punishment, and the criminal is just another maximizing consumer, without any kind of social embeddedness or psychological realism. Therefore we only have to increase the price, and demand will fall. In certain contexts this is relatively close to the truth, e.g. in the case of white-collar crime, where the underlying assumptions seem to be more realistic, but in other cases, considering all the social aspects of criminality the theory badly fails. The average real criminal misperceives the probability of getting caught 33 as well as does not always care too much about the severity of the
27 As someone put it hanging with zero probability. 28 For example as originally proposed by Becker. See also Stigler (1970). 29 Becker (1968), Cowell (1985), Witte and Woodbury (1983) 30 E.g. Rubinstein (1979) and Greenberg (1984) 31 A rare exception is Graetz et al. (1986) 32 Pyle (1983) summarizes the empirical finding up to date. 33 See in Varian.
- 22 - punishment: the legal system is rather remote for most people.34 Moreover, as we will see in the sociological and legal review certainty has significant side-effects backing up the normative climate of the society, resulting in lower criminality. Societal and psychological effects are of major importance in real world crime, but these are impossible to address without departing from the neoclassical framework and methods.
1.1.1.4. Criticism
As with all theories, there are two basic ways to criticize the Neoclassical Paradigm. The first accepts the underlying assumptions, and considers what the theory is incapable to explain basing on them. The second assesses the assumptions themselves. We have already touched upon both. First, as mentioned, supposing the correctness of the basic tenets, there is no guarantee that the outcome will be socially just. Second, there is no answer for how the market clearing prices form. This is why there is a need for a hypothetical auctioner, who compares supply and demand and picks the equilibrium price. In real markets we rarely find anything like this. The need for a more dynamic approach is even more compelling if we consider that there is no solid reason that ensures that there is a unique equilibrium. On the contrary, in the modern economy above all generalized increasing returns can generate multiple equilibria more and more easily35. The role of the state in the neoclassical framework is quite ambiguous. On the one hand it could fill the room for the auctioner – which it seldom does. In fact it was tested, mainly in centrally planned economies, but it did not work properly. Actually, if neoclassical assumptions were true, central planning should have proven much more successful:36 the state could just be the right institution to aggregate information and set the right prices using its authority. This could have meant that markets were not free any more, but all actors has already been seen as price takers which poses a question on how much freedom for markets is really needed in the static view of Neoclassical economics. The paradigm was unable to present a convincing argument against central planning and state ownership. States on the other hand were perceived as ‘the’ means of correcting for market failures. Truly, state has a unique ability to make actors play inferior strategies (from their own point of view, not society’s), and thus circumvent the free-riding problem. Although this often works, it is not a panacea mainly because of lack of information and interest, rent seeking and all drawbacks of bureaucratic control. This is the reason why many authors seek new means of governance, and hope to find in the form of communities that often appear to complement markets and states successfully. Taking into account the extremely abstract model of the economic man and markets, there is ample ground for attacking the theory at its assumptions.37 First for the actors: real people’s psychology is much more complex than that of Homo Economicus. They are far from being omniscient, their information sources, memory and mental capabilities are limited. They are opportunistic, their preferences are volatile and they are subject to many sorts of social and commercial influence. These issues will be covered in more detail later. Second,
34 E.g. Salem and Bowers (1970) 35 E.g. in Varian Ch. 34. 36 As Bowles cites Stiglitz in Ch. 14: „if the neoclassical model would have been right, market socialism would have been a success and central planning would run into far fewer trouble” 37 Probably the most basic reference for criticizing the Neoclassical image of economic man is Simon’s seminal paper on Bounded Rationality (1955). Cullis and Lewis (1997, p308) is also useful, giving a brief summary of faults in the orthodox picture.
- 23 - markets are much more complicated and faulty than treated by the orthodox theory.38 To mention only a few examples contracting is costly, contracts are often incomplete, borrowing is limited, (constraining engagement in otherwise lucrative contracts for the poor), labor markets show strong signs of reciprocity between employers and employees (resulting in involuntary unemployment), market information is limited and markets are often incomplete (leading to that certain goods cannot be traded by the willing). And most of all, enforcement is not free − at least not the way the neoclassical school presupposes. The importance of the neoclassical model and its results by now lies not in the faith that its assumptions or predictions are correct to any degree of universality. It has been, however, the first economic model that pointed out how large scale phenomena – a general equilibrium – can emerge from local interaction, and it has been the first line of thought that attempted to tackle seemingly everlasting economic problems. By now it stands as a starting point for models relaxing its various assumptions, and as a benchmark to relate results with. We also must acknowledge that there are circumstances where its assumptions are good approximations of reality and where its results may still apply.39
1.1.2. Information Economics, Transaction Costs
The next step towards a more realistic model of economy incurred a shift in the basic axioms. Both the image of the actors and markets have been modified. The following table has been adapted from Kreps (1990), Ch. 20. It shows the dimensions along which the main departures from the orthodox model have taken place and the corresponding theories.
Self Interest Without Guile With Guile Utopian Rationality Information Complete General Equilibrium Economics Team Theory Temporary Transaction Cost Bounded Equilibrium Economics Behavioral Evolutionary Methods
Table 1. - Departures from the Neoclassical Model of Homo Economicus
As it can be seen there are two main directions along which different theories modified the original assumptions on the economic man. The one on the horizontal axis deals with the supposed nature of his self interest. As termed by Kreps, ‘Utopian models’ gave up this central tenet completely, and let the people be driven by other motivations. We do not discuss team theory herein, but other and process regarding preferences show up frequently in evolutionary models, too. The original model of economic man however selfish he was, at the same time was a perfect gentleman without opportunism or guile40. Relaxing honesty but
38 See e.g. Bowles and Gintis (2000) 39 E.g. on markets like the stock exchange. 40 Or was he only deterred by costless enforcement of complete contracts? It is mostly a matter of taste how you see it, but I think I prefer the above one.
- 24 - retaining selfishness, and combining it with incomplete contracts and bounded rationality, where information is not perfect or not free any more raises the issue of transaction cost economics.41 At the same time the two branches of information economics stems from the opportunism of agents and informational asymmetries42: difficulty in monitoring after settling the contract gives rise to moral hazard, and asymmetric information before engaging in business generates adverse selection. On the vertical axis complete rationality is relaxed to various degrees. Boundedly rational people are still trying to maximize or accomplish some goal by discerning optimal action to a degree allowed for them by the environment or their own imperfection. Behavioral agents, however follow behavioral rules, which may or may not have anything to do with maximization.43 The behavioral rules can originate in as diverse sources as some kind of learning from personal experience, social influence, habits and traditions or genetic heritage. Behavioral models describe the behavior of agents directly without digging into the mental processes that induce it. Because of the diversity of the factors that can affect behavior a standard model of bounded rationality has not emerged yet, and probably never will: probably the most we can say is that some motives are more important in particular situations than others, and try to map these linkages as accurately as we can along with the interplay between the motives when they are at work simultaneously. My present work is a step in this direction.
1.1.3. Strategic Interaction
Another way of extension concerns the way people interact. In the standard model economic actors are simply price takers whose actions do not affect prices, therefore agents’ individual decisions do not alter the possibilities of others. There was one exception that we touched upon earlier, namely externalities, but then the third party was only passively suffering from causes beyond his reach. The new idea is to allow actors to interact strategically, actively modifying each other’s possibilities and best responses. It is the field of classical game theory,44 a pivotal point in development of economic thought, which also came up with its own ideas for cooperation. It is an important link between the old school and the behavioral approach: on the one hand much of its methodology and terminology is used in experimental studies, especially when it comes to testing the validity of the stringent restrictions most old models are built upon. On the other hand it is a stepping stone towards the evolutionary movement and behavioral approach. The most basic strategic games use one shot games with two players, and retains the old selfish, omniscient, and forward looking stereotype for players. People choose their moves basing on complete information, this time however, they have to take into consideration how the other party will react to their actions. The solution concepts emerging in this context –
41 Which in turn helped to open the neoclassical black box and to create a better understanding of firms and cooperation within it. (Starting with Coase (1937)). Besides see Simon (1951) on the incompleteness of the employment contract. 42 In this sense their rationality is bounded, but only in this sense: they use whatever they have optimally. 43 It is probably easier to capture what it means for people, but firms also can be treated as behavioral entities. The orthodox tenets about determinants of firms’ behavior can be relaxed to various degrees. First, managers can have different goals than maximizing the profit of the firm (see the literature on the principal-agent problem), they may want to maximize other things than profit, e.g. market capitalization, revenue, etc…, or they may not maximize at all. Even in Kreps (1990), one of the standard textbooks in microeconomics there is a behavioral model for firm behavior (p731). He also calls for better models of bounded rationality in a dynamic setting where agents learn from past experience (p772) − evolutionary models for short. 44 See for example Kreps (1990), part 3.
- 25 - dominance and Nash-equilibria – are just as static as those of the neoclassical model, so we face the same problem: the theory is incapable to choose between multiple equilibria. Thus, lacking dynamics in the basic framework solution can only come from outside the theory in the shape of focal points, conventions, pre-play negotiation, etc… There have been many extensions to the original concepts. These on the one hand further relaxed the restrictions on players and on the other hand introduced new types of games and new solution concepts. First, perfect information was abandoned giving rise to information sets, expected utility maximization and beliefs. Second, game theoretic methods were applied to games with more than two players, which cast new light on some old problems. For example markets can be seen now as an n-person game where each firm could do better by coordinating their price policy, but all has an incentive to defect.45 Another well- known example is the ‘Tragedy of Commons’, basically a multiple player game, where Pareto optimality and Nash equilibrium do not coincide, which destroys cooperation. (Observe that this is again an externality – free rider problem.) Third, repeated play was found to be able to explain cooperation relying on selfish motives only, where in the respective stage-games mutual defection is predicted. In other words if it is possible to threaten the other party with future defection, cooperation can be secured. This concept is important because it has been a chief candidate for deducing pro- sociality from selfishness. However, this kind of solution only works when games are played indefinitely, and the discount factor is sufficiently high (close to 1)46. The other problem is that this way there are again many possible equilibria between which the theory cannot distinguish. This famous result is called the Folk Theorem, pointing towards further extensions of the model and opening for social factors like norms, learning and reputation.47 Fourth, new solution concepts 48 have been created. The most famous of them is probably sub-game perfection, which dismisses all Nash-equilibria that do not produce Nash- equilibrium in every suitable sub-game. Another invention is trembling-hand perfection which only accepts solutions as valid where small errors in action does not destroy the equilibrium. Sequential equilibrium incorporates beliefs into game theory, where to decrease the number of acceptable equilibria, those where not all the available information is used are rejected. Another noteworthy technique is to set aside strategies that harm the credibility of threats. What should be noted is the tendency for a more complex and less perfect image of players.49 Fifth, games also can be approached form the behavioral direction. If we relax the forward looking calculator model of players, we uncover a whole new world, where imperfect players are able to learn from past experience by trial and error gradually improving their
45 in Bowles Ch. 14. 46 Since a discount factor close to zero effectively turns a repeated game into a succession of one-shot games. 47 One cannot speak about repeated games without summoning Axelrod’s renowned tit-for-tat strategy (Axelrod and Hamilton (1981)). Another examples also addressing some societal considerations using informational imperfection and reputation are Dixit (2003) and (2004). The social model therein is, however, extremely abstract for the sake of analytical tractability. (Infinitely many agents located on a circle and paired randomly.) Another remarkable attempt is by Kandori (1992) showing the efficiency of community enforcement relative to bilateral threats. (The reason is that their so-called contagious punishment, the possibility that one defection can trigger a complete breakdown of cooperation, increases the threat against defection.) They also examine the role of reputation and selective punishment. Besides, the paper contains some useful references to earlier research on repeated games. 48 Also in Kreps (1990), part 3. 49 Classical game theory also tried to address irrationality by introducing randomness in player’s actions, although in the real world ‘irrationality’ most often appears as systematic deviations from the predicted behavior. Refer to the results of experimental economics later.
- 26 - decisions, where they can utilize local information, where they are prone to social influence and have motives that surpass narrow selfishness. This movement puts the strictly strategic nature of interaction into doubt, and emphasizes behavior as opposed to mentality. This new area of game theory is called evolutionary game theory,50 an intersection of the evolutionary approach and game theory in Economics. The richness of possible forces that may influence economic action is an unlimited source of research in this area. It also requires new techniques, because complexity of internal motives and external interaction often renders analytical inference impossible − simulation is often inevitable. My model can also be used to experiment with different strategies in an evolutionary fashion. There is one more notion in the more recent game theoretic literature that needs to be mentioned, also because it is closely related to the change of social norms. When strategic complementarity is present, playing certain strategies may increase the utility that other players get if they choose to play it (a quasi-externality again). This in turn generates a positive feedback in the number of players playing such a strategy. The economic aspect of this phenomenon is generalized increasing returns, where the utility from having a good depends on how many other people own it.51 This phenomenon further pierces the validity of the classical theorems of general equilibrium by generating multiple (punctuated) equilibria and therefore path dependence in markets. Its sociological precipitation is norm cascades which means that norms tend to change abruptly followed by long periods of stability.52
1.1.4. Experimental Economics
Recognizing the complex nature of human motives and interaction there is a new area emerging in economics dedicated to the empirical research of economic decisions and action. It is called Experimental Economics. Whoever plans to build a realistic model nowadays cannot avoid getting familiar with its results. In this section after getting a look at the methodology, I am going to introduce the most important findings it confers for enforcement, punishment and sustainment of pro-social behavior.
1.1.4.1. Experimental Methodology
Economic experiments are usually carried out by engaging subject in simple economic games whereby playing well they can earn money or credits that are later converted into money. It is a crucial requirement that real stakes be used, preferably tailored to the normal income of the players, to make incentives credible. For most of these games game theoretic predictions are easy to find, which is also important because the goal of most studies is to investigate how people’s behavior relates and often deviates from the theoretic predictions. The majority of the studies have been undertaken in the controlled environment of laboratories, where people usually interact through computer interfaces. (There have been a number of field studies, too, when experimenters visited remote places to examine possible
50 A good recent book on the topic is Gintis (2000). Hofbauer and Sigmund (1988) is another fine reference. A very famous example of evolutionary games is the so-called Hawk-Dove game (Smith (1982)), where instead of individual players choosing their actions strategically, a population of individuals following either of two different behavioral rule sets are considered, with a focus on the proportions of the players with distinct strategies. 51 E.g. the telephone. 52 For the economic phenomenon see Varian Ch. 34. For norm cascades refer to the sociological part herein at page - 58 -.
- 27 - cultural differences.) What I would like to emphasize at this point is that players in experiments are usually deliberately isolated from each other and placed in an artificial environment to prevent informal social influence and keep pressure measurable. This way societal pressure is mostly reduced to monetary penalties.53 Among others the so-called Public Good Game is an important tool used by experimenters. I would like to describe this in more detail because its setup is similar to my simulation tool developed herein. In a PG game there are a group of people simultaneously deciding how much to contribute to a public good. After each player indicated his contribution and the total amount is paid in, it is multiplied by factor (greater than one, but smaller than the number of players) and paid back to the players in equal shares. It is basically the well-known public good situation familiar from the introduction. The dilemma of the players is that zero contribution is a dominant strategy for everyone regardless the action of the other players. The game is usually played repeatedly. In this version, results are usually partly in line with the game theoretic predictions: even though in the initial rounds contribution is significantly greater than zero (usually between 40 and 60 percent), it swiftly deteriorates as the game progresses. However, there are many variants to the basic game that show more dramatic deviations. First and foremost, there is one when in each round a second stage is inserted after payments are over: people can punish each other having the other’s contribution revealed to them. This extension made the PG game and its variants the primary tool for experimental research on peer punishment, and has cast light on many important anomalies that standard theory cannot explain.54 Another widespread variant of the game is the so-called Common Pool Resource Game, when instead of contributing, players can withdraw from a common pool of a predetermined amount of credits or money. This situation resembles more closely to what we have seen with ‘The Tragedy of Commons’. The difference between this and the previous game is that paying in elicits a positive, while withdrawing a negative externality on the others. The Common Pool game also comes in many varieties. Besides, there are many different treatments for both games, controlling what information is revealed to the players, who can punish whom, if players are paired randomly or systematically in the subsequent rounds and so on. What treatment is implemented depends on what aspect of the punishment phenomenon the experimenter focuses at.55 The punishment phenomena being the primary focus of this dissertation, now I am going to summarize what experimental results tell us about it.56 1.1.4.2. Punishment and Contribution in Experimental Economics
By today there is overwhelming evidence57 supporting that people are willing to exert punishment on others, especially on defectors of norms and shirkers even when it is costly for
53 Friedman and Cassar (2004) is a nice introduction to experimental methodology. For a pivotal field study that was carried out in 15 small scale societies and demonstrated important cultural variability see Henrich et al. (2001) 54 Carpenter (2004) lists many references concerning pool (public good) games. 55 See e.g. in Carpenter (2004b) for more on pairing protocols (partners, strangers, complete strangers) and Kosfeld and Riedl (2004) for references and summary on varieties of these games. 56 For a more extensive summary and starting point of references please refer to Decker et al. (2003) and Carpenter (2004b). Kosfeld and Riedl (2004) is also a good source for punishment studies. 57 Falk et al. (2001) is a widely referred source on experimental evidence on costly punishment. It also discusses the possible motives behind this kind of behavior. Besides, it contains a summary of how empirical research on the topic progressed and also refers to related theoretic models. Kosfeld and Huck (1998) and (2004) also cites many references.
- 28 - them.58 Punishment in turn seems to be able to sustain cooperation in many settings when standard theory predicts general defection. For example in PG games the usual deteriorating picture we get without punishment reverses if players are able to monitor and punish each other, thus shirkers respond sensitively to peer pressure. Moreover, this result seems to be quite robust across different treatments of the game. 59 The most important patterns experiments found concerning costly punishment are as follows.
● Although inelastic to both price and income, punishment is sensitive to price, and the demand for it varies similarly to an ordinary and inferior good.60 This result suggests that however flawed the original image of Homo Economicus is, selfishness is ubiquitous. ● Perfect strangers – players that are guaranteed not to meet again in a repeated game − are punishing each other like partners, who are paired in every round, which undermines the efforts to explain punishment by selfish motives and strategic action. ● People also punish players (to a lesser degree, though) whose defection do not affect them.61 ● The demand for punishment can be so strong that it lowers overall efficiency even accounting for the rise in cooperation.62 ● Defectors react to punishment by increasing their contributions. While in PG games without punishment average contributions usually converge to zero, when an alternative for voluntary (and normally costly) punishment is available, contributions does not diminish and in many settings converge to full contribution.63 ● Even informal sanctions influences free riders, but monetary punishment is more effective.64
58 Punishment when it is costly is a typical a public good, therefore standard theory predicts undersupply. One possibility to explain it is to suppose that it is costless, because in this case everyone can gain individually by exerting punishment on shirkers. However, the cost of punishment is hard to define. In standard experiments there is a monetary cost that players have to pay if they choose to punish, basically they can buy punishment, but the overall cost in real-world settings can be much more complex. Opportunity costs, losing of further cooperation and softer notions like social confrontation come also into play. Moreover, punishment can also be rewarding either internally (by a so-called “warm glow”) or externally by peers. What is more, punishing also can be an instrument of signaling, to show future partners that the punisher is a ‘good’ type as far as reputation is an issue. (This controversy in literature on the costly or costless nature of punishment is the reason for my model features a dedicated parameter for it.) See e.g. Elster (1989), Friedman and Singh (2000) and Kosfeld and Huck (1998) for more information on this topic. 59 The standard reference is again Falk et al. (2001), but Carpenter and Matthews (2004) is also a good source regarding the effectiveness of punishment on shirkers. 60 Carpenter (2004b) and Carpenter et al. (2004) 61 Carpenter and Matthews (2004). They coin the expression ‘Social Reciprocity’ for punishment on violation of widely held norms. 62 Decker et al. (2003) and Fehr and Gahter (2000) suggest that allowing for punishment is not always wealth enhancing. See Cinyabuguma et al. (2004) for possible efficiency loss caused by excessive or misdirected punishment. 63 While this reaction is likely to be in great part strategic, Bowles and Gintis (2000b) and Fehr and Gächter (2000) find evidence that defectors tend to raise their contributions directly after getting punished, which suggests that psychological effects like (aversive) conditioning represented by the direct effect in Contributron play an important part in conducting human behavior also in economic situations. 64 Masclet et al (2003) and Carpenter (2004b)
- 29 - ● Some studies suggest that severity of punishment received seems to be correlated with the relative difference from average contribution rather than an absolute measure.65 ● Even the mere possibility of getting punished has an effect on contribution.66 ● Older people, men, higher contributors and norm motivated people tend to punish more. People who studied Economics punish less.67 ● While in the western world punishment and cooperation patterns appear to be rather uniform, there is field evidence on cultural diversity in small scale societies.68 ● People are willing to punish in the last period of the game.69 (Again, does not make sense for strategic motives) More specially, in the last period defection raises suddenly but punishment follows it – that is people do not punish strategically but expect others will do so.70 ● Results vary, but it seems that there are distinct types of people with respect to cooperation and punishment behavior (and most likely motivations).71 ● Community pressure appears to be more effective than personal punishment.72 ● Rewarding is generally less effective than punishment.73
The natural question considering the anomalies discovered by experiments is what causes people to act virtually against their best interests? The whole idea of costly and voluntary punishment is rather perplexing for followers of the neoclassical doctrine since it seems to be an inferior strategy to free riding on others’ punishment. In spite of the evidence on the non-strategic nature of punishment, many still try to use the old ideas and explain it through selfish motives and strategic action. In enumerating the possible motivations utilitarian ideas are apt to be placed first. In principle, those who punish non-contributors (or more generally violators of widely held norms) may still act in their own (redefined) interest. 74 On the one hand there is a possibility to see everything that people do increase their specially redefined utility. Proponents of this view say that everything we do we do it because we draw utility from the very fact that we do so directly, or through some psychological phenomenon like self- justification or a preference for consistency. This approach, however, invalidates the notion of utility, turning it into a mere tautology. Next, people may punish to increase their future income or to secure credibility for their threats − in other words for selfish reasons. Indeed,
65 Fehr and Gachter (2000). Interestingly, people are sometimes punished even if they exceed the prevailing group norm of effort, especially when this signals that others should increase their effort likewise. 66 Fehr and Gachter (2000) 67 Carpenter et al. (2004) and Decker et al. (2003) 68 Henrich et al. (2001) 69 Falk et al. (2001) 70 Carpenter and Matthews (2004) 71 The percentage of types has been displayed for example in Carpenter (2004b). Gachter et al. (2003) compare the proportions in a cross-cultural study. Falk et al. (2001) also suggest this, along with Bowles (2003) Ch. 3. 72 E.g. Carpenter (2004a) finds that “free riders seem to be more likely to dig in their heels to spite one goodie- goodie who criticizes them, but, at the same time, they bend to follow a collectively established norm.” In Decker et al. (2003) experimenters compared an individual and three collective punishment schemes. It turned out that players preferred collective schemes, but within it the weaker ones, mainly because collective rules allowed for higher profits, but at the same time it harmed personal freedom (players had to pay for punishment even if they did not like to.) 73 Sefton et al. (2002). The reason for this is that people can be conditioned to fear from the possibility of punishment while rewarding must me carried out continuously. Another factor can be the kinky and relative utility function from prospect theory. 74 See Elster (1989) on why people engage in costly punishment and more generally on why they follow norms.
- 30 - there are strong signs that self-regarding motives play a central role in many situations. For example in ultimatum games offers tend to approximate a share that maximizes the player’s expected payoff given the probability of rejection. In PG games there is usually a large minority free riding irrespective to what others do.75 Moreover, that in dictator games offers are low 76 , that productivity of the public good influences contribution 77 , plus the price sensitivity of punishment78 all point to that self-regarding motives are clearly present in most economic situations. Many studies have proven, however, that at the very least they are not the only significant factor that drives human beings in economic situations and punishment activity.79 Falk et al. (2001) report that from three main motives they examined in their experiments strategic reasons turn out to be the least significant as a determinant for informal punishment. It was followed by spitefulness80, which was still relatively weak as compared to the third, fairness, which turned out to be the strongest motive by far. Fairness is also a composite notion: The retaliation motive over others being unfair appears to be more important than achieving a fair payoff distribution. In my model fairness is the primary factor conceived to motivate people for punishing defectors. Many other authors emphasize the importance of non-strategic or emotional motives. 81 Altruistic reasons have long been a candidate for playing a part in economic action. Altruism in a punishment context means that one would punish to increase the well-being of others in his group who also suffer from the defection. This motive, however, does not seem to be too considerable, at least in its unconditional form and among the non-kin.82 Reciprocity and its subtypes, however, are more prevalent in social and economic interaction. Simple or personal reciprocity is coupled with self interest 83 while strong and social reciprocity, salient issues in theory, are closer to fairness. We will learn more about reciprocity in the next section. A crucial question for using experimental results in modeling real life is how economic experiments correspond to behavior outside the lab. Naturally, real life behavior and empirical observations serve as the basis for designing experiments. There is strong evidence and many examples coming from various areas of economic life that people differ from the pure model of Homo Economicus. They are myopic, they are liable for inconsistence in inter-temporal choice, their preferences are variable84 and they are susceptible to social pressure, etc…These observations of course are rather crude and require scientific justification. Many of them induce theoretical models, too, which subsequently call for experimental validation. This is one leg of the relationship. The other important question is whether players in a laboratory environment behave similarly to their everyday conduct. There is some evidence that they do85 but this is still an open question, especially when it comes to societal connections. Conspicuously, most
75 Fischbacher et al. (2001) 76 Hoffman el al. (1994) 77 Carpenter (2004a) 78 Carpenter (2004b). He notices that even ‘principled cooperators’ tend to give up at some point as the price of punishment increases. 79 E.g. Falk et al. (2001) on the primarily non-strategic motives behind informal sanctions. See also Güth et al. (1982), Güth and Tietz (1988) and Ochs and Roth (1989), but there are many others. 80 Spitefulness is defined as a negative valuation of other player’s payoff regardless of their behavior. 81 For instance Decker et al. (2003) lists many of them while he also finds them to be important. 82 E.g. Bowles and Gintis (2000). 83 Refer back for example to Axelrod’s tit-for-tat strategy where reciprocity is coupled with a threat of future defection. 84 E.g. Thaler (1991) 85 Glaeser et al. (2000)
- 31 - experimental studies neglect, or deliberately rule out informal social context, so that they can concentrate undisturbed on the psychological motives within people. Even when experimenters are talking about ‘partners’ treatment people are partners at most for the duration of the experiment. Players in many cases interact through computer interfaces, ruling out real informal pressure. The information they have on each other’s actions are also strictly controlled. Particularly, in most experiments subjects are not allowed to know how much the other players have punished shirkers to prevent conformism.86 Conformism, however, is a very strong social phenomenon and it is unlikely that it would not have a substantial effect on shirking and punishment. There is a wide range of sociological literature that we will soon encounter supporting the pervasive nature of conformism, and results of rare experiments also suggest its power87. The fact that experimenters often explicitly control against information flow and personal contact suggests that they also suspect that it would significantly distort their results. That people are allowed to transform their emotions and normative sensitivity into financial penalties is certainly more realistic than the old models of neoclassical economics for a social setting, still, laboratories where people can interact through computer screens and keyboards does not necessarily capture the whole spectrum of behavioral motives. 88 Although economic experiments make a substantial contribution to economic psychology, neglecting real social connections, informal pressure, and thus much of norm dynamics and conformity has still left ample space for empirical research.89
1.1.5. Behavioral Economics
Behavioral Economics is the area where real life observations and experimental results on economic behavior induce formal theories. It represents the second big step in relaxing neoclassical assumptions: having allowed for rationality to be bounded by human imperfections and environmental constraints now rationality itself becomes subject to reexamination.90 The central idea of behavioral economics is giving up maximization as the basis of economic behavior, and turning to behavioral rules themselves which may or may not find their origins in any kind of optimization. Behavioral patterns can also come from long term evolutionary processes, personal experience and social interactions. In the view of the area behavioral rules begin to gain independence from actors, they compete, spread, mutate and shrink in their virtual living-space, just like biological species in the real ecosphere. It also
86 From the above referred works at least in Falk et al. (2001), Decker et al. (2003), Carpenter (2004a) and Carpenter (2004b) subject were not allowed to know about how others punished shirkers. 87 Remember that informal pressure appeared effective even without monetary punishment involved. 88 There are a couple of issues that might distort the real-life correspondence of these experiments. I would like to draw attention to it to the extent of a footnote, because I have nowhere seen it written down and I feel it might be significant. It is that when experimenters tell participants that there are two things you can do in this experiment: cooperate and punish, participants probably feel more encouraged to act, because having only these enumerated options or do nothing they are likely to exercise them just to “try them out”. In other words just by listing them the possibilities they are probably communicated to a certain degree that they are expected to do something. In real life this kind of influence does not exists. Secondly, in these experiments subjects only lose a small amount of monetary income, while in real life the cost of punishment is much more complex and probably more painful. Moreover in the lab subjects lose something that is not theirs yet. Compare this with Prospect Theory’s relative utility and see that this may result in a weaker retentivity. 89 As mentioned there were a few experiments that let real informal pressure take effect, but systematic research on how willingness to punish and shirk can spread in social networks is still missing. 90 Please refer back to Table 1. The prologue of Bowles (2003) is a very nice introduction to the most important features of the behavioral image of economic man. Thaler (1991) is also a good source on how rationality is bounded in decision making, incorporating papers on fairness and experimental economics.
- 32 - implies that agents are not bound to follow the same fixed rules for ever: people adapt to their environment, follow different rules as they gain experience and are able to improve91. On the other hand if people can change it is reasonable to suppose that society is heterogeneous, where different behavioral rules contest simultaneously, and people following diverse behavioral rules live side by side interacting and influencing each other. The latest image of Homo Economicus is diverse and versatile.92 Nevertheless, one should also note that there has not yet emerged a generally accepted standard model, and because of the multitudes of possible motives most likely it never will to any comparable extent to the neoclassical model. Although the model of economic man has been heavily modified, an important part of the economic heritage is retained. People still live constrained by scarcity and their behavior is shaped by it, this time, however, not by rationalization but evolution. Inferior strategies wane not because agents can calculate they are bad, but because of selection. The selecting forces can be diverse, including biological (players with worse strategies produce less offspring) and social ones (people tend to copy certain strategies93) or they can be based on personal experience (trial and error learning94): agents trying to improve consciously have become backward looking. It is even possible that some inferior strategies or traits survive because they are connected to advantageous features or because they were useful once so they could proliferate and got hardwired into the genome or culture and today they lack competition. Another retained feature is that in most models large scale outcome still results from uncoordinated interaction.
1.1.5.1. Behavioral Concepts to Explain Pro-Social Behavior
Behavioral models offer new ideas to explain pro-sociality. Below I review the most important concepts. As a matter of fact metanorms are not a real behavioral explanation because it tries to track back the origin of socially beneficial behavior to self interest. It essentially assumes that there are certain agents who punish not only shirkers, but those who do not punish shirkers, this way making punishing a dominant strategy even when it is costly otherwise. This attempt, however, does not solve the problem since in such a setting a new public good emerges: punishing the non-punishers. Certain models react to this by creating additional layer of punishers who punish those who do not punish non-punishers, and so on to infinity. Empirical studies, however, do not support this idea.95 It is important for us, because it is another sign of that punishment is not driven by self-interest. In fact even a second layer is rare in reality,
91 If one prefers to explain behavior from internal motives, changes in behavior can be approached via endogenous preferences. In addition to their variability, the old notion of preferences is extended in a variety of ways the most important being social, other regarding and process regarding preferences, each able to explain different behavioral anomalies. 92 This methodology is not restricted to human agents. Firms or other groups of people can be modeled much the same way, and with substantially greater flexibility than with neoclassical tools. It is a different question that firms are not subject to many human traits (like emotions) and this is why they are easier to see as maximizers. See footnote 43. 93 There are many propositions what kind of strategies: the most successful, the most common, the longest surviving, those of similar people, etc… See e.g. Axelrod (1997) Ch. 3. This process can be intentional, but much of social conformism takes place unintentionally, even unnoticed. More on this in the sociological part. 94 Its importance in real life is emphasized by sociologists. Ostrom (1990) writes: “the only reasonable assumption to make about the discovery and calculation processes employed is that [common pool resource] appropriators [i.e. agents in a cooperation – defection dilemma] engage in a considerable amount of trial-and- error learning.” Axelrod (1997) Ch. 3. also underlines its significance. 95 Sethi and Somanathan (1996), Lopez and Luck
- 33 - although there do exist some examples: so-called Honor systems96 in certain colleges, legal obligations declaring not to report certain offences as illegal, some cases in international politics or certain phenomena in lynching crowds.97 It is very likely that metanorms alone cannot solve the problem.98 One of the oldest explanations to cooperation is altruism.99 Indeed, there are examples for this kind of behavior, but it is manly restricted to the relationship among the kin. This observation is paralleled in biology where kin selection and inclusive fitness are central for explaining proliferation of genes inducing altruistic behavior towards the genetically related.100 More puzzling is non-selfish behavior towards the non-kin. It would require either unconditional altruism, for which there is little evidence, or so-called reciprocal altruism, which is basically the same as the selfish version of reciprocity – not really altruism. There are also propositions to include certain kinds of social preferences into the utility function, e.g. inequality aversion.101 Nevertheless, how such sentiments could come about is still an open question. Strong and social reciprocity comes up with a possible answer. Another important class of models tries to use different variants of reciprocity. Reciprocity as we have seen is able to sustain cooperation in repeated games. In this case reciprocity is a masked threat of future defection, therefore if someone punishes a shirker by returning defection his motive is basically selfish.102 This basic kind of reciprocity, however, cannot support cooperation in n-person games, as in such cases returned defection hurts cooperators, too, and leads to general defection.103 A possible solution is the introduction of some kind of reputation which allows targeted punishment104. Nevertheless, incentives to punish remain a problem even then.105 There is a different class of reciprocity, however, more closely related to altruism and the philosophy of my model, which seems to be working in larger populations, and also delivers an answer for the incentive problem. The idea is that humans have a natural inclination towards punishing defectors. Two remarkable sorts are Strong 106 and Social 107 Reciprocity. Strong reciprocity is where “members of a group benefit from mutual adherence to a social norm, strong reciprocators obey the norm and punish its violators, even though as a result they receive lower payoffs than other group members”. Social reciprocators108 in contrast “punish free-riders even in groups to which they can neither contribute to nor benefit directly from”. In the case of Strong Reciprocity voluntary punishment is conceived to be based on biological evolution, most likely on group selection, and it is now supposed to be part of our genetic information. Social Reciprocity on the other hand is explained to stem from social norms. As we have seen,
96 Salem and Bowers (1970) 97 Axelrod (1997) Ch. 3. 98 Henrich and Boyd (2001), however, shows that an arbitrarily small amount of conformism can stabilize a multi layered punishment scheme, because the amount of punishment required decreases fast as we move upwards on the layers. 99 With other-regarding preferences altruism can be given a selfish-like complexion. Indefinite expansion of the notion of utility, however, obscures what we call self-interest. 100 See Allison (1992) for a short summary and Hamilton (1964) for sociological consequences. 101 See e.g. Bolton (1991) 102 This form of reciprocity is sometimes called the Weak form of reciprocity. E.g. Bowles and Gintis (1999) 103 More references for this in the introduction to Axelrod (1997) Ch. 3., See also Fehr and Fischbacher (2003) 104 These two sorts of punishment are also known as direct and indirect sanctions. Indirect sanctions are for example defection and exit that is those which are not targeted, unlike direct sanctions. 105 See Kandori (1992) for models with and without reputation. 106 Bowles and Gintis (2003), and Gintis (2000) 107 Carpenter and Matthews (2004) and Carpenter el al. (2004) The latter also compares the two kinds. 108 In fact these two notions are very similar to Malinowsky’s generalized reciprocity, whereby someone reciprocates for defection suffered by a third party.
- 34 - experiments support that people are willing to punish even if it is not directly beneficial to them, and the above quoted papers convey additional evidence. While these schemes are related to altruism, they are not exactly the same: in the case of altruism agents punish because they have good intentions and think they can do good to others by punishing. At the same time with strong and social reciprocity they do so because they are governed by intrinsic impulses (emotions)109. The behavioral difference is that in this case punishment is exerted even when there is no chance that it will improve others’ well-being, for example in the last period of repeated games.
1.1.5.2. The Evolutionary Methodology
Although behavioral models often employ evolutionary reasoning, not all of them do so. Evolutionary explanations110 are mostly applied when we try to reach for an explanation on the origin of certain behavioral phenomena that are not readily deduced from self interest, as we have seen with strong reciprocity for example. The old school did not need such an approach, because self-regarding preferences had been so strongly tied to survival that it seemed evident that everything on earth must be selfish. Today, for the same reason it is a bit trickier and demands deeper insight to find a way to infer non-selfish features from survival or occasionally other selecting forces. Voss (2001) summarizes the key elements of the evolutionary approach:
● Boundedly rational agents, erroneous responses111 ● Stochastic dynamics, stochastic shocks, mutations ● Recurrent social interaction ● Focus on long run behavior
We have already discussed the first point, but have not spoken so far about the second: the importance of random events in the evolutionary approach. It is clear that in biological evolution in order that selection can work and adaptation emerge mutations are necessary. If we intend to build our economic models on evolution we are bound to give chance a key role. Chance can enter our models in various ways.112 They can occur in the form of inheritable mutations that can be handed down to the offspring – as with strong reciprocity −, they can be behavioral innovations coming from various sources − imperfect perception or replication, personal innovation, etc… − or from other chance events like random matching. Whatever the selecting force is, it needs an underlying variability to operate on and we need a mechanism in our models to generate in. Recurrent social interaction gives rise to the competition among different behavioral patterns: agents can compare, copy or select rules by interacting with and observing others. In certain models (e.g. those based on biological evolution) this aspect is not explicitly given as there the selecting force is not choice but survival. Another important notion is the employment of local rules and interaction. Classical economics used representative agents and even in evolutionary game theory mean field approach and random pairing is common even
109 An interesting addition is Sethi and Somanathan (2003) on reciprocal preferences. 110 An early source of importing biological reasoning into Economics is Becker (1962) 111 We can add that in the way I have presented terminology behavioral agents are also subject to these models. Voss probably uses the word to indicate that agents are not perfectly rational. 112 Bowles (2003) Ch. 2. also see Ch. 14. for a very nice comparison of neoclassical and evolutionary methods.
- 35 - though it is not very realistic. Instead of being restricted to comparative statics, agent based simulations, make explicit network modeling possible with diverse agents in the nodes, and allow the modeler to observe the dynamics of the system. In turn, stochasticity with a large number of diverse and adaptive interacting agents give rise to the emergence of large scale patterns or even dynamic equilibria which is much more natural than the static picture of general equilibrium.113 Finally, evolution − as opposed to the instantaneous responses of rational agents − is a slow process, no wonder long-run outcome is in the focus.
1.1.5.3. Evolutionary Game Theory
These new concepts were introduced in the first place by game theory, which in search for solutions for its problems − to explain cooperation and equilibrium selection − found the evolutionary methods promising.114 This led to the birth of evolutionary game theory.115 The new area on the one hand required the abandonment of hyper-rationality and approached players from an evolutionary direction, seeing them as adaptive, backward-looking agents, who are able to change their strategies dynamically. On the other hand game dynamics become the key target of analysis. It helps to understand how certain coordination problems are solved, and see the processes that determines which of the equilibria (that look equally conceivable from a static point of view) is selected finally. Because it is a wide area I can only mention the most important concepts and tools of the field. They are important because they have been used widely in models of pro-sociality. First of all new solution concepts appeared. The most important is probably evolutionary stability116 that is a Nash-Equilibrium, which is also stable to small fluctuations in strategies due to mutations in the population. Being an equilibrium concept it is primarily used in static analysis. Replicator dynamics 117 on the other hand specifies the population dynamics of strategies with different survival value basing on differential replication. Differential replication means that more successful strategies spread faster due to selective forces either biological or cultural. In game theoretic models success is measured by payoffs, and this kind of updating is also known as payoff-biased replication. In analytical models to calculate the change in strategic proportions between consecutive rounds it is common to assume random pairing of players,118 and switching strategies with a positive probability if
113 A large number of locally interacting entities can generate emergent phenomena that mean field methods cannot capture. Starting from mathematics and cellular automata through chemistry to social psychology and finance this general notion appears in many disciplines. See e.g. Wolfram (2002) for cellular automata. In addition Cohen and Stewart (2000) is a really thought provoking and entertaining book on complexity and chaos, touching upon many areas. 114 Please refer back to footnote 50 for references. 115 As the Stanford Encyclopedia of Philosophy remarks: “In the preface to Evolution and the Theory of Games, Maynard Smith (1982) notes that "paradoxically, it has turned out that game theory is more readily applied to biology than to the field of economic behaviour for which it was originally designed." It is perhaps doubly paradoxical, then, that the subsequent development of evolutionary game theory has produced a theory which holds great promise for social scientists, and is as readily applied to the field of economic behaviour as that for which it was originally designed.” 116 Introduced by Smith and Price (1973). It has been applied to many evolutionary games, including the Hawk- Dove game. 117 Taylor and Jonker (1978), Zeeman (1979) 118 Taylor and Jonker (1978). In certain anonymous market situations random pairing or the other widely spread strategy, comparison with the population average can be realistic, but in most social settings social networks give a better model of interaction – and a harder time for obtaining analytical solutions.
- 36 - comparison shows possible improvement. Some models in order to consider switching costs also use a threshold describing the required difference between the successfulness of the old and new strategy. Another renowned idea of biological origins is multilevel selection or group selection. It emphasizes that if there are relatively exclusive groups of cooperative agents competing with each other, then selection does not necessarily operates only at the individual level: successful groups can outcompete other groups. This consequentially allows for the survival and proliferation of socially beneficial traits even if they are individually costly.119 Such traits of course involve non-selfish motives and more specifically internal motives to punish free riders. This constitutes the core of some models in need for an explanation of social sensitivity, like for example Strong Reciprocity. Importance of social groups in biological selection also links genetic and cultural evolution as tightly as no other theorem before. One remark needed that has relevance to the present work. In most evolutionary models concerned with the development of non-selfish punishment there are different kinds of agents – like for example cooperators, free riders and punishers − resembling to the typification proposed by experimental studies. Basically, these agents have two distinct features: either they free ride or not and either they punish or not depending on their respective types. The relative share of different types in the population moves according to their relative success − either on an individual or group level that is both free riding and punishing is shaped by success. 120 However, if we consider what experiments say about motives to punish we see that if punishment is variable, it is not likely that it is governed by success in the short run at least, right because there was a long-term evolution in the past described by evolutionary models that undermined prevalence of egoism in this respect. This boils down to that if we want to build a model of short-term cultural evolution, using the same kind of reasoning as in long-term biological evolution is not the right thing to do: we must consider different motives for shaping willingness to punish.
1.1.5.4. Evolution of Institutions
In neoclassical economics markets were taken as given. In game theory the rules of interaction including assumptions about information distribution, the possibility to issue threats, the pairing rules of players and the like were also exogenous to facilitate obtaining results. Although they have a substantial effect on the outcome 121 − some of them were probably reverse engineered exactly in order to explain certain outcomes − not too much effort has been spent on investigating how these institutions122 were established, whether they were set up intentionally, they evolved spontaneously or if they really existed at all. In evolutionary economics even institutions become endogenous, the rules of the game
119 Boyd et al. (2003) for example show that it can support altruistic punishment. 120 Examples include Carpenter and Matthews (2004) and Bowles and Gintis (2003) 121 Remember for example voting rules, where the outcome can depend upon the order in which the questions are posed. Furthermore, in game theory many games use special criteria (sequential or simultaneous moves and information sets, pure or mixed strategies, beliefs, etc…) largely influencing the conclusions that can be drawn from the analysis. Focal points, conventions, preplay negotiation and the possibility to threaten with defection are also crucial assumptions in equilibrium selection and coordination problems. Also refer to the externality problems and the importance of well-defined property rights. 122 Institutions in evolutionary terminology indicates all kind of factors that determine the rules of interactions, starting from formal institutions like the legal system, through markets to social norms, etc…
- 37 - themselves changing in the process of evolution123, casting light on their origins − and a shadow of doubt on their optimality. If something is shaped by evolution although there is a force towards melioration, more exactly better adaptation to the selecting force, there are a number of pitfalls that can impede reaching the global optimum. First, the selective force can be too weak to weed out inferior solutions. Second there may not be enough variability to constantly recreate competition. Third certain improvements may require too many changes at the same time, an evolutionary leap, or in other words breaking out from a local optimum. Fourth even evolutionarily superior variants can be marginalized because of the sheer number of the prevalent phenotype. And fifth, certain bad features can be cross-linked with advantageous ones so the eradication of the former would also discard the latter. We can add that even the selective forces can change in time, so if one force swept the system into the proximity of a local optimum in terms of another, the new force will not be able to move it away and reach its global optimum.124 Community governance owes its present popularity partly to the evolutionary movement. As theory points out communities of adaptive agents may be capable to develop and maintain their rules of conduct independently and regulate their members for the benefit of the group. There are empirical examples125 for groups solving difficult coordination and free-riding problems without any resort to external authority. Community governance is hoped to be able to cooperate with institutions more familiar to classical theory, markets and states.126 The strength of communities lies in their unique ability to locally monitor behavior and enforce pro-sociality. As economic experiments suggest they have all necessary features to carry out this task: people are willing to deliver punishment to defectors and defectors tend to bend to peer pressure. It is already clear, however, that community governance also has its limitations. For example it appears to work better in smaller ‘close-knit’127 communities than in larger groups, it may burden inter-group relationships by leading to parochialism, and peer punishment may lead to excessive consequences for defectors. The interpersonal relations and thus the forces affecting people in social groups are much more complex than the plain picture of pure market connections of Neoclassical Economics, even than the strategic image of Classical Game Theory. A whole new assortment of notions must find their place in the new models: reputation and trust, pride and shame, vengeance, respect, and most importantly norms are all promising candidates to supersede or at least complement greed: there is still much to do. The present work is also devoted to create a tool that may contribute to the
123 Adaptive agents also have endogenous preferences. See e.g. Bowles and Hopfensitz (2000) for co-evolution of institutions and preferences. Kreps (1990) Ch. 14. also highlights the importance to explore the origins of institutions. 124 Although Cohen and Stewart (2000) is concerned more with biological evolution, many of their ideas is usable for its cultural counterpart. Bowles (2003) Ch. 2. also refers to some of these limitations of evolutionary development. 125 Sociologist Ostrom (1990) discusses various real-world examples on how communities managed to overcome situations described above. She also points out that authorities have the possibility to affect the price of enforcement by recognizing or rejecting local rules. 126 Economist Bowles is a strong proponent of community governance as a complement to markets and states See especially Ch. 14 in his 2003 book which summarizes their relationship and the most important features of the former. 127 The notion of ‘close-knit’ group stands for small, highly connected and homogenous groups with diffuse social relations, where prospect on power usage is credible, information on reputation is readily available and long term reciprocal connections are possible. In close-knit groups therefore deviations are easily detected, sanctions can be less costly to deliver and can be exerted by multiple agents, thus threats are more effective and pro-social behavior is less difficult to enforce. As proposed by many, close-knit communities are also a cradle for social norms. See e.g. Voss (2001).
- 38 - understanding how the deeply intricate structure of community governance works and interacts with centrally deployed authority. For these new forces to be effectively harnessed for the advantage of society, economic science must first acknowledge their existence and then carefully examine their functionality. I have written economic science because much of these notions have not been unknown for science as such. This is the reason for the next chapters attempt to give an insight into other social sciences which are already familiar with our novel concepts.
1.2. Psychological concepts
Much of the relevant psychology behind pro-social behavior has already been presented under the results of experimental economics. In this section I would like to draw attention to the most basic psychological theories that has influenced the images of man of other social sciences, and whose propositions are implicitly part of my model, too.128 I am going to introduce shortly the behaviorist and cognitivist approaches. It is followed by a brief discussion of additional psychological phenomena bearing relevance on cooperation in a society of diverse agents that has been omitted so far: origins of altruism and selfishness, sources of mental (and through it behavioral) diversity, the psychological aspects of conformity and the so-called by-stander effect. Behaviorism is one of the oldest theories in modern psychology and one that still has considerable appeal. It has been founded on the principle that scientific research of the mind should be based on objectively observable facts, in the first place on behavior. In this respect it has common roots to classical economics, which were also satisfied with a minimalist mental model of mind and based its inference on operationalized data. Nevertheless, what behaviorism has supposed about the mechanisms governing behavior is very different from that in classical economics. Behaviorist psychologists saw every kind of behavior resulting from conditioning: an outcome of successive rewards and punishments, which communicate with individuals how to adapt to their environment. If we put this next to what has been said about experimental economics and the evolutionary movement we witness how this old theory find its way at last into contemporary Economics.129 As proposed by the Behaviorist Theory, there are two fundamental ways of conditioning.130 The first is classical conditioning, by which an organism learns to connect a previously neutral stimulus to another by repeated pairing, and begins to react to the first similarly to the second. Classical conditioning is central for generating guilt (the reason behind self-punishment in my model): the previously neutral experience of misbehavior is paired with bad feeling by repeated application of punishment. 131 The second is operant
128 This section is based on Atkinson et al. (2000) 129 Of course in evolutionary models punishment and reward is not the only source of adaptation, which also involves biological pressure for survival, and conscious comparison of success. Thus for example behaviorist theory is connected to evolutionary methods on the one hand by their common idea of adaptive agents, and on the one hand there is the evidence on the effectiveness of peer punishment and social pressure resulting in many times subconscious conformism to norms (thus underlining the relevance of conditioning). In addition Social Learning Theory emphasizes learning by observation, which is more closely related to cognitive comparison (though it is doubtful if even in this case adaptation results from conscious decisions). 130 On both kinds of conditioning and complex learning: Atkinson (2000) Ch. 7. 131 There is a similar phenomenon closer to the cognitivist side of Psychology: cognitive dissonance. A drive for cognitive consistency can also keep up pro-social behavior, this time however, resulting from a conscious pursuit of consistency between attitudes (possibly planted by social norms) and behavior.
- 39 - conditioning when certain responses are learned because they operate on the environment. Operant conditioning points to the situational dependence of behavior: as feedback can be different in different situations, behavior also tends to vary. In my model operant conditioning gives the theoretical basis for the direct effect of punishment.132 Social Learning Theory is a relatively new area connected to conditioning. It puts more emphasis on vicarious learning or learning by observation, which means that individuals need not necessarily be conditioned directly, they are able to imagine expectable consequences by considering examples they see, which can substantially facilitate socialization.133 Another issue closely related to the present model is the so-called aversive conditioning134, where a certain behavior is weakened by delivering repetitive punishment for it. Psychologists stress, however that punishment in itself although inform about what not to do, does not give an alternative and this is why can be less effective that rewards. Moreover, to be effective punishment should be exerted consistently and immediately after the behavior took place. Punishment also can be harmful because it might entail undesired side-effects like fear of the situation when it is received or the person who exerts it. The other major psychological school I need to touch upon is Cognitivism. Its central tenet is that mental processes and thus human action is chiefly based on cognitive phenomena including reasoning, planning, decision making and communication. The original image of Homo Economicus is most closely engaged with this area. Originally this school built its theories on introspection (as contrasted by behaviorism), by today, however it has moved to constructing mental models, that describe how information is processed and transformed into actions.135 Cognitivists find the source of human diversity in the differences between these mental models in different individuals. Besides, for cognitivism learning is not an automatism like conditioning – it is more in line with the so-called complex learning. Nowadays most psychologists agree that the complexity of human mind cannot be reduced to a degree where it can be explained by one or another school alone. The different branches of psychology are better seen as focusing on different aspects of the same phenomena, each bearing a seed of truth without excluding each other. Even though emphases vary, psychology today sees people as adaptive, conditionable and rational beings at the same time, who also have hardly modifiable unconscious motivations and are influenced by biological processes, too.136 My work follows this line of thought.
1.2.1. Individual Traits
132 Recall that direct reactions to punishment have been observed in economic experiments (footnote 63). 133 It is a possible way for expansion of my model. So far seeing punishment does not changes propensity to shirk. It would require at least one more parameter to incorporate it (e.g. by making its effect be a fraction of direct punishment), which is left for future extension. (Nevertheless, seeing punishment can change propensity to punish, but that is elicited by conformism to a social norm.) 134 Atkinson (2000) p. 250. A short notice on the classification of conditioning forces: they can be either positive or negative reinforcers: something pleasant or removal of something unpleasant, or positive or negative punishment: something unpleasant or removal of something pleasant. 135 It also uses computer models of the mind to simulate mental functionality, which was first proposed by Herbert Simon in the late 1950s. See e.g. Simon and Clarkson (1960) and Simon and Gilmartin (1973). 136 Psychoanalytical and biological approaches have not been covered here, but see Atkinson (2000) Ch. 1, 2 and 13. A quotation taken from p 625 is especially instructive in conjunction with my model: behavior is “determined many factors other than attitudes […] one obvious factor is the degree of constraint in the situation […] Peer pressure can exert similar influences on behavior.”
- 40 - Altruism and selfishness – two central notions of economics – have their own literature in psychology, too. According to this altruism can originate in a multitude of phenomena and it generally depends on the respective schools which one of the causes is taken to be most important. Altruistic acts may be supported by empathy, or it can come from semi-selfish motives nurtured by incentives like social approval. Social norms, reciprocity and genetic reasons are referred, too,137 and cultural causes are also able to strengthen or weaken altruistic tendencies. Nevertheless, what is more or less agreed upon is that for altruistic motives to arise in personality a care-giving environment is necessary together with appropriate cognitive development. As for selfishness arguments are quite similar to those in economics: selfish genes, kin selection and reciprocity. There are, however, observations and not only in humans138 that indicate a surprising level of empathy and non-selfish behavior, which parallels experimental findings in Economics. It has been mentioned that for evolutionary economics Homo Economicus is “diverse and versatile”. To provide support for this I would like to tell a couple of words about the sources and development of individual differences as Psychology sees it.139 The two main sources of differences are the genotype and the environment. They are not independent of each other, as for most children parents provide both and parental genes also affect the environment the family lives in. The dynamics of personality development, however, is more complicated. First, by the so-called reactive interaction the child’s personality extracts different elements of the environment − that is depending on personality people tend to perceive and evaluate the same experiences differently, so they will have a different effect on them. Second, by evocative interaction different personalities invoke different feedback from their environment. Third by proactive interaction the developing personality actively controls its environment and the stimuli it receives. These three elementary factors of psychodynamics reveal how small initial differences in personality are amplified and lead to significantly differing adults. In addition, there is abundant evidence on the limited capacity of human minds either in perception, memory and intelligence.
1.2.2. Social Psychology
The fact that social environment strongly moulds our behavior and personality is maybe the strongest law of Sociology, and it also begins to infiltrate into Economics. Psychology provides explanation how and why people react to social contact. Conformity is a basic and very strong human feature.140 I need to go into a little bit more detail as conformity and imitation are basic elements of updating in my model. There are two basic levels of it: when someone does not agree with the influencer and does not change his beliefs and attitudes is called compliance. In other cases people become convinced changing their beliefs and attitudes, in other words they internalize the opinion of the
137 Some evidence cited for it are that babies often start crying when they hear other babies crying and that toddlers show distress seeing other people in trouble. Atkinson (2000) Ch. 18. 138 For example among chimpanzee by-standers sometimes approach the victim of an attack to give comfort to him. On reciprocity between chimpanzee: Watts (2002) 139 In more detail Atkinson (2000) Ch. 12. 140 The most frequently quoted experiments to illustrate the strength of conformism is Asch’s (1955, 1958) where subjects (one at a time) were placed into a group of confederates who gave a common – but obviously false – answer for some trivial perceptional question. The results were striking: 75% of the subjects conformed at least once, and even those who dissented showed strong signs of distress.
- 41 - influencer.141 Thus, when someone internalizes a position or social norm, on the one hand continuous surveillance and external enforcement is not necessary any more and on the other he becomes a potential disseminator of the norm. Most typically people tend to conform to the majority.142 There are two main possible reasons behind this act: the first is that it may be the case that someone supposes that the majority must be a better source of information than his personal experience. This is called informational influence. The other reason, normative influence143, is more social: someone alone defying the common opinion runs the risk of isolation, social disapproval and exclusion from the group. In this sense attitudes serve a social adjustment function by helping us feel belonging to a community. For the same reason consent serves also as a signal of membership − sometimes so strongly that the actual content becomes completely secondary. Conformity is the basis for the social updating in my model. Conformity is even stronger within one’s reference group. Reference groups are “groups with which we identify; we refer to them in order to evaluate and regulate our opinions and actions”. Nevertheless, somebody does not necessarily identify himself with only one reference group, and he does not even have to be a member of it. These groups are usually those whose members we respect, and would like to become similar to. This is why with respect to reference groups conformity is likely to turn into internalization when dissent or difference initiates an internalized punishment. In addition, when we are actually members of the group the threat of exclusion is much more severe, which leads to even stronger incentives to conform. Conformity consequently causes these groups to converge. (Observe the interplay between forces of convergence and divergence in the development of the personality.) Communities, especially when they are ‘close-knit’ enough to serve as a form of governance will likely be reference groups at the same time as they need the extra strength that these groups provide for regulation through conformity and internalized motives. This explains why these groups tend to be homogenous and warns us for the possible danger of parochialism. Finally, I have to mention a special kind of social influence, which is also referred by some economic models. The so-called by-stander effect144 is people’s willingness to intervene for third parties, especially when affected by a social context. In other words it describes whether someone is more or less ready to give a hand to someone else when he sees that there are others around them exerting certain behaviors, or how willingness to punish reacts to the same. The theory and evidence is rather controversial on this issue. On the one hand there are many possible reasons why people can be reluctant to interfere with alien affairs: the physical danger, to avoid getting involved in suspicious cases, and the lack of ability to act quickly. Moreover in the presence of others there are additional factors: one might happen to misinterpret the case and make fool of himself, another reason is the activity or indifference of others and diffused responsibility. On the other hand people seem to be more willing to intervene if they see others doing so, besides such actions can well be a signal of being a good type. Some economic theories like e.g. Social Reciprocity advocate people’s responsiveness and there is also some empirical evidence to support it.145 Other studies are more skeptical.146
141 Atkinson (2000) Ch. 18. 142 Minority influence and obedience to authority are two additional forms of compliance. The latter can be linked to the expressive function of law, and together they constitute the basis of the effect of central punishment on propensity to punish in my model. 143 Axelrod (1997) terms the effect of conformity on social norms ‘Social Proof’, and cites the same two reasons to conform. 144 Conformity and the by-stander effect are only the most relevant types of social influence. Other important forms include social facilitation (changes in performance in company) and deindividuation (crowd behaviour). 145 Carpenter and Matthews (2004) See also what has been said about willingness to punish at a cost. 146 See Latane and Darley (1970) on increasing reluctance to help when others are around.
- 42 - The by-stander effect points to that willingness to punish is not indifferent to social circumstances. (Recall the discussion about economic experiments controlling against social context.) This is one reason why my model features parameters for social influence on propensity to punish.
1.3. Sociological Concepts
The image of the social man has been fundamentally different from the economic man for a long time, in spite it is the same being after all. The usual argument for this strict fissure is that these are different aspects of life governed by different behavioral laws and even if there is some faint interference between the two, we do not lose too much by applying the scientifically necessary abstraction. Drawing a solid borderline between these two fields, however, is a great responsibility − and the anomalies presented earlier suggest that the traditional separation was not entirely successful: we need a more flexible demarcation. The following table147 summarizes the main differences between the two archetypical models of man:
Homo Economicus Homo Sociologicus
Associated with Adam Smith Emile Durkheim Pushed by quasi-inertial Orientation Pulled by outcome forces Guided by Instrumental rationality Social norms Adherence to prescribed Source of dynamics Individual maximization behavior Mindless plaything of Social embeddedness Asocial atom societal forces Table 2 – Comparison of Homo Economicus and Homo Sociologicus
The two most closely related sociological concepts to the present work are social networks and social norms: my model simulates a group of arbitrarily interconnected adaptive agents, whose interactions are governed by social norms. Both of these notions are quite new to economics: the role of social norms was largely neglected for a long time because of the socially sterile image economic man, and social networks were hard to capture with the traditional methodology. For conceptual clarity, and to reflect on the knowledge accumulated on them by Sociology I am going to discuss them in this chapter. In the first section we are going to get an overview of social networks. We search for an appropriate definition, and summarize the most important hallmarks of these networks. Next a few remarks are given concerning how social networks can be represented in formal models, and the role of computer simulations are emphasized in this respect. Then we turn to the relevance of network connections and their structure, and finally we call attention to the so-called punishment networks.
147 Based on Elster (1989)
- 43 - In the second section we move on to study social norms. We begin with considering how Economics attempted to approach them. Then the most important approaches to define and classify them are summarized. In turn we bring up two examples that are specially related to the topic of the dissertation: norms of cooperation and enforcement. We familiarize ourselves with the possible roles of social norms, whether they are necessarily advantageous at the individual or the societal levels. Next enforcement of social norms is discussed, which is an issue when a social norm is instrumental on the societal level but adherence is not necessarily directly beneficial to the individual. Subsequently we examine the emergence and distribution of social norms and point out two typical phenomena of norm dynamics: norm cascades and inertia. Afterwards we collect the possible limitations of social norms in maintaining pro-social behavior, which can be useful when it comes to comparing them to other types norms. Finally, as a pass-through to the following section, which discusses legal norms, we consider the institutionalized forms of enforcement.
1.3.1. Social Networks
Social networks and its analysis have a large literature148 by today, from which I can only present the most substantial issues here. Probably the shortest definition for network is “an interconnected system of things or people”. 149 A bit less brief delineation of social network is “a set of actors that may have relationships with one another. [Social] networks can have few or many actors (nodes), and one or more kinds of relations (edges) between pairs of actors.”150 We can see that notion of social networks is a subset of a much broader area of networks. (Or rather its intersection with Sociology. Hence, there is a link to many rather far-fetched looking fields that have also something to do with networks.) The most important attributes of social networks are151:
● Interdependence of agents ● Linkages between agents constitute channels for information or resource flow ● Network connections provide opportunities or constraints on individual action ● Stable network structure, enduring social connections
The hallmarks of social network analysis152 are:
● Concentrating on the relationship between actors rather than their individual attributes ● Captures emergent phenomena ● Emphasis on effects of network structure on outcomes
148 http://supernet.som.umass.edu, the homepage for “Supernetworks” is a good starting point for social networks containing many downloadable articles on networks, including classical ones and links to several journals and other resources. A brief textbook on the topic is Scott (2000). A short introduction is Sola Pool and Kochen (1978), which is a classical article, a very clear text. 149 Taken from WordNet: http://wordnet.princeton.edu 150 Nagurney et al. (2004) 151 Adapted from Wassermann and Faust (1994) 152 From Steve Borgatti: http://216.247.125.88/networks/whatis.htm
- 44 - When modeling social networks, there are a number of simplifying assumptions that are usually made. First, structure. There are many methods to generate artificial social networks. Maybe the simplest is to use random networks where the (ex-ante) probability that a link exists between two nodes is independent from which nodes they join. This setup, although easy to analyze and derive analytical results for, not very realistic. However, randomness can be constrained in many ways to give topologies more resembling real life. For example it is easy to create so-called hierarchical or scale-free networks.153 Conversely, many models use completely regular tessellations, like nodes arranged on a line or circle.154 Rectangular lattices or toruses are also popular, however, they are mostly used with mobile agents, who can change their position (and therefore connections) along the runs of simulation.155 Real-world networks are somewhere in between: they show certain randomness and structure at the same time. One of their important characteristics is clustering: there are groups of people with dense within-group network and relatively few external connections.156 This implies that for the average agent a neighbor of a neighbor is more likely to be a neighbor than another average agent. This variety of theoretical assumptions inspired me to make custom network setups available in my model. The second group of simplifying assumptions concerns with the quality of connections. In real life, as the above definition suggests, there are many kinds of connections − e.g. kinship, professional, affectional and informational relations, etc… − while their strength also varies. In spite of this, in most models there is only one, all-or-nothing type of link. Furthermore, connections are mostly symmetric that is if one agent is connected to another, the other is also connected to the first.157 A few methodological highlights. The mathematical area most closely connected to social networks is graph theory. There are many attributes of networks, mostly related to connectivity that can be obtained by standard mathematics. (Examples are probabilities of connectedness, the number of certain cycles, etc…) 158 Nevertheless, if we would like to examine dynamics in social networks, especially with semi-random networks (that is those with certain type of restricted randomness) and more complex agents, the only viable choice is simulation. Computer simulation is a flexible tool able to handle very complex dynamics, enabling social scientists to test hypotheses and do experiments that would be not practical, ethical or possible in real-world experiments. 159 Finally, social networks are conveniently represented by a matrix (also known as the Moreno matrix), which facilitates certain calculations about the network. It is also useful because it allows representation of asymmetric connections of different strength in one unified structure. What are the consequences of network connections in society? Firstly, as already referred they influence information distribution. Unlike the markets of neoclassical economics, where every information is instantaneously available in full accuracy to every participant, in real life the spreading of information is quite often obstructed, and restricted to specific channels. Social connections constitute an important channel for all sorts of private
153 Stocker et al. (2002). It is worthwhile to call back that random pairing routinely used in game theoretic appliances is a statistical method resulting in a new set of connections in each turn that is, in effect, a model without social structure. It is not the same as random networks (which are lasting formations). 154 Examples include: Kosfeld and Huck (1998) for linear, and Epstein (2000) for circular models. The former is an analytical, the latter is a simulation model. 155 E.g. Epstein and Axtel’s (1996) Sugarscape uses a torus. 156 A related issue is the famous small-world problem that is how randomness and order affect the connectivity of networks. Two basic links are Kleinfeld (2002) and Travers J. and S. Milgram (1969) 157 The above mentioned paper by Sola Pool and Kochen (1978) discusses this issue as well. 158 A classical reference is Gilbert (1959) 159 Gilbert & Troitzsch (1999)
- 45 - information. As mentioned above other resources − credit, workforce, etc… − can also be passed over along these links, as determined by the structure of social networks. Secondly, social connections are also a means of interaction and influence. They are the vital substance of thoughts, memes, role models and social norms, living their own life in this virtual space, and governing human action and interaction in the real world.160 When a given rule in society becomes sufficiently widespread and develops an enforcement mechanism we talk about social norms. Not surprisingly, social networks play a crucial role in the emergence of norms.161 Social norms are more likely to emerge when people are closely related, therefore, the quality and density of these links are essential determinants of the normative atmosphere of communities.162 In addition, and even more closely to my agenda, some authors coin up the idea of punishment networks 163 a network through which peer pressure is delivered, similarly to my model. The real-world significance of social network structure is reflected by their similarly strong effect on simulation results.164 As demonstrated earlier cultural and biological evolution are interconnected, in other words social structure has a hold even on our genome.
1.3.2. Social Norms
From a sociological point of view, social norms are the primary driving force of people, having almost the same prevalence as selfishness in economics. In the light of empirical evidence on the power of norms it is largely justified. Social norms, and not only personally useful ones, not even socially useful ones survived and influenced the life of many for centuries without external support or outrightly against powerful attempts to eliminate them.165 It is not surprising that social norms have a huge literature, and a wide assortment of theories that try to make sense of them. On the one hand this variety comes from the multiplicity of different schools in Sociology, and on the other hand from the heterogeneity of norms themselves. In this section I try to give an overview of how sociology see norms − a fundamental element of my model − touching upon their nature, dynamics and role in society.
1.3.2.1. Social Norms in Economics
160 Starting from Durkheim (1897), through Dawkins (1976) until the recent theory of Evolutionary Culture Theory the history of social contagion theory spans more than a century now. 161 Emphasized e.g. by Putnam (1993) and Hechter and Opp (2001) 162 At the same time the broad notion of social networks does not specify the strength of the links. Certain authors stress explicitly that not affection, but connection is the defining characteristics of communities, e.g. Bowles (2003) Ch. 14. Of course, it depends upon the way someone defines community, my personal view is that,however, for community governance to be effective, a certain level of identification with the group is indispensable, because it provides much stronger susceptibility to peer pressure. 163 Carpenter and Matthews (2004) 164 Zheng (2002) 165 Popular examples include foot-binding in China, dueling in Europe and female genital mutilation in Africa. To illustrate the power of such norms, it is instructive to read the following quotation: “Female Genital Mutilation (FGM) is a cultural practice that started in Africa approximately 2000 years ago. It is primarily a cultural practice, not a religious practice. But some religions do include FGM as part of their practices. This practice is so well ingrained into these cultures, it defines members of these cultures. In order to eliminate the practice one must eliminate the cultural belief that a girl will not become a women without this procedure”, http://www.members.tripod.com/~Wolvesdreams/FGM.html
- 46 - To begin with it is necessary to tell a few words about how classical Economics approached norms in the rare cases it did. In fact, there seemed to be a “norm against norms” among economists which had kept this important factor successfully apart from the analysis of economic decisions. Basically, even when economics acknowledged the existence of norms, and considered their role, it did so using its traditional rationalistic toolbox: it supposed that people follow norms out of rational calculation, treating social norms as a kind of commodity entailing certain costs and benefits for the individual, or an instrument to increase social efficiency. 166 Game theory seems to be the most appropriate field in Economics to deal with norms. 167 In a game theoretic terminology norms can stabilize if compliance is a Nash-equilibrium. To secure this and make compliance an optimal strategy, in the case of personally disadvantageous norms an enforcement scheme is necessary, which either by some kind of threat or actual punishment ensures conformity. This conjures up the familiar issue of extended utility functions, metanorms, repeated interaction, close-knit groups168 and the Folk Theorem with all the problems we met investigating the possibility of whether and how selfish means are able to support pro-social behavior: how to explain conventions without external punishment or seemingly explicit incentives to breach, how to overcome costliness of punishment, how to predict outcome when multiple equilibria are possible169, and so on. As social norms can – and often do – support pro-sociality, it is no wonder that selfishness encounters much the same problems maintaining norms as pro-social behavior directly. In fact, social norms are sometimes used as an acronym for pro-social behavior, even though they are not necessarily positive for society.
1.3.2.2. Definition of Social Norms
Turning to the sociological approach to norms, it is convenient to start by defining them. Or at least try to collect the most important attempts at defining them. The main difference between these definitions is that they put emphasis on different aspects of norms. There are four main classes of definitions. The first underlines norms’ ‘normative’ nature and states that they are rules paired with their enforcement mechanisms. 170 This definition suggests that norms constitute a constraint on individual action by affecting personal incentives, through which affecting social outcome 171 – quite an economic aspect. Nevertheless, to precisely delineate the notion of social norms, it is also necessary to distinguish it from other norms and rules and restrict enforcement to exclude legal and
166 Which is similar to the functionalist approach in sociology. In fact, advocates of community governance also see norms as potential instruments of efficiency gain. The difference is that they do not insist on tracking it back to individual maximization. An interesting example on how economic models can be applied to social norms is Roback (1989) (referred by Cullis and Lewis (1997)) who has an interesting model in which individuals can invest into altering the price of conforming to a social norm. By the way, in a sense, people do exactly this when they punish defectors at a cost. 167 See e.g. Voss (2001) 168 Emergence of norms can be easier in these groups because of their ability to monitor behavior and punish deviance more effectively, while at the same time (as reference groups) shape preferences, beliefs and attitudes. Refer back to footnote 127. By the way, when selfish incentives seem sufficient to explain the appearance of norms, economists talk about endogenous, when only the equilibrium is in focus, exogenous emergence. 169 For which a better understanding of norm dynamics would be necessary, an area that received relatively little attention until recently. 170 When a rule is not enforced it is sometimes called convention. In many cases, when social norms or conventions solve coordination problems the built-up practice is self-enforcing in the sense that no one has an incentive to decline, which is mostly enough to keep it alive. Refer for example to how the world is stuck up with the QWERTY keyboard. 171 It is called the bottom-up definition in Eggertsson (2001).
- 47 - economic coercion. 172 Secondly, norms can be seen as moral imperatives 173 or values followed by a great number of people, which emphasizes the internalizedness of norms, that the great majority of people follow these rules by conviction. Thirdly, norms can be approached through their effect on behavior: sometimes they are also defined simply as behavioral regularities174 in a population. The advantage of this approach is that behavior being an objective phenomenon, it is readily observed without any reference to soft concepts or introspection. The disadvantage is that regularity can result from other things, for instance − to not go very far − self-interest. One further possibility is to highlight the expectations stemming from these regularities. Most contemporary authors, however, combine the above parts, and some of them add extra remarks. Principally, it is stressed that for a norm to exist it must be followed by sufficiently many people, which also implies that the existence of a norm is a matter of degree.175 This will gain even more relevance when we come to the dynamics of norms. Others emphasize emotions (that is irrationality) and behavior as the definitional elements of norms.176 In my work I also adopt a composite definition, acknowledging that there can be diverse reasons behind someone’s adherence to them and norms’ prevalence in society − including economic rationality, social conformity and psychological automatisms. Another way that helps to narrow down any idea is demarcating it from similar notions, that is laying down its differentia specifica. In life there are many kinds of norms and rules that are not social norms.177 There are rules of profession, personal habits, conventions, etc… There is not enough room here to consider all of them, but I would like to highlight one special kind of norms and specify its differences for social norms: legal norms. It is important to consider them as the legal system is the most complex and widespread institution that societies use for organizing and enforcing pro-sociality. Moreover, their certain characteristics apply to other social institutions, and they also heavily interact with social norms. (This interaction is built into my model.) The following table compares the main features of social and legal norms, and a forthcoming section summarizes the interplay of the two norm systems.
172 However, as we will see there is a significant interplay between the legal system and social norms. 173 E.g. in Homans (1951) 174 As used e.g. in Axelrod (1997). 175 Like in Axelrod (1997). This is important for my model, too, as agents can change their propensity to contribute and punish gradually both at the individual and network levels. 176 Like Elster (1989). He also promotes emotions as connected to norms. 177 When in the text I use the word ‘norm’ for the sake of shortness, I mean social norm unless otherwise stated.
- 48 - Social Norms Legal Norms
Rules Informal, diffuse Formalized, exact
Appearance Verbal Written Formalized creation, Institutions No formal institutions application and enforcement Enforcement Distributed, informal Centralized, formal
Practiced by Anyone Professionals Slow, high inertia, with Dynamics Faster, smoother occasional cascades Development Organic, evolutive Designed, purposive
Table 3 – Delineation of Social and Legal Norms178
1.3.2.3. Classification of Social Norms
I have already remarked that there are many kinds of social norms. From our point of view probably the most important categorization is which divides them into internalized and shared (externally enforced) norms. 179 Observe that this parallels the two kinds of psychological conformity: internalization and compliance. The difference is that this time we look at the same phenomenon from the point of view of norms, the ‘memes’ that spread in a population, and not that of the individuals. The reason this distinction is crucial is that it fundamentally changes the nature of norm subsistence. While shared norms require external enforcement (which, as demonstrated, is quite problematic at least from an economic perspective), internalized norms are internally enforced by feelings of guilt and anguish in case of violation.180 In all probability, a certain degree of internalization is necessary for a norm to exist.181 On the one hand those who internalized it will not need to be forced to comply, on the other hand they are likely to become enforcers who make the rest of the group comply. Nevertheless, it would be hard to find a norm that is universally (and unconditionally) internalized: there are always violators and a need for enforcement. One important effect of internalization is heavier inertia: change in behavior governed by rules followed only out of compliance can be very fast relative to the case when people are driven by conviction. The process of internalization is influenced by many factors: arguably for example it is usually easier to internalize norms that do not conflict with self interest from the outset. 182 While norms can be internalized without external imposition, the primary mechanism that plants them in our minds is socialization.183 Socialization can be defined as
178 Partly from Opp and Hecthter (2001) ‘Institutions’ is used in the common meaning of the word. 179 Coleman (1987) 180 Voss (2001) notes that internalized enforcement helps mitigating the Prisoner’s Dilemma problem by transforming it into a so-called Assurance Game. 181 Argued for example by Cooter (1996) 182 More on the role of interests in Horne (2001). 183 Remember for example how guilt is established by parental conditioning.
- 49 - the process of learning of values, norms, attitudes and culture needed to function in a group or society, which is often aided by socializing agents: parents, friends, school and the media.184 Socialization can be achieved to serve particularistic interests like media socialization or that stressed by Marx,185 however, with most norms this is the means of teaching individuals how to live together in a community. Further classification involves conjoint and disjoint norms186: a norm is conjoint when the target and beneficiary group of the norm are the same, and disjoint when these groups are different. There are conditional and unconditional besides prescriptive and proscriptive norms. Moreover norms can be divided into universalistic and exclusionary kinds, the latter being norms of a smaller group, furthermore dyadic and communal norms depending on the number of people involved in the relationship regulated by the norm. To put the two norms in my model into this picture, they are both conjoint, prescriptive and universalistic norms, the contribution norm being shared, conditional and communal while the punishment norm being internalized, unconditional and dyadic.
1.3.2.4. Examples: Norms of Cooperatrion and Enforcement
A few examples follow to illustrate norms’ relevance in controlling pro-social behavior. First of all there are norms of cooperation187, including several variants: a norm of altruistic cooperation requires cooperation when it increases the utility of fellow group members. It is close to the Kantianist kind, which requires cooperation when it is reasonable to assume that it would be socially beneficial if everyone succumbed to this norm. A conditional cooperation norm, however, only expects reciprocation. More closely to my agenda, certain authors talk about norms of tax compliance,188 based on a more general form of cooperation norm. Still others mention contribution norms 189, a more abstract form of personal sacrifice in the interest of the community. The norm requiring contribution from agents in my model is closest to this last one. The other sort of norms I would like to bring up here is enforcement norms, an instrument of social pressure. To start with norms of reciprocity and retribution are related to this notion, 190 as they also serve to secure a threat against free-riding. However they are different, as reciprocity also includes returning kindness while retribution is dyadic. The idea of an enforcement norm appears in various places: enforcement norms can serve as a secondary norm serving primary norms’ subsistence.191 Under the term of sanctioning norm another paper stresses their importance in the establishment of norms.192 Yet another study characterizes ‘principled cooperators’ the dominant type found in an experiment as “subscribing to a sanctioning norm” 193 Others use memes instead of norms to present a
184 Following Moschis and Moore (1982) 185 The socialization of the lower classes by the higher ones to accept the status quo. See also Michael Moore… 186 Coleman (1990) 187 Elster (1989) 188 Elster (1989) quoting Laurin (1986) 189 Carpenter and Matthews (2004) 190 Elster (1989) 191 Maher (1998) 192 Opp (2001) 193 Carpenter (2004b). He also gives a description of individuals with that norm: they are less sensitive to price changes of punishment (i.e. they are more norm driven), they do not punish in order to increase group welfare (i.e. not altruistic), they punish even if they do not cause free-riders to cooperate (not outcome oriented). He also touches upon the idea in some of his older papers: Carpenter et al. (2004) and Carpenter and Matthews (2004)
- 50 - similar phenomenon: a meme spreading in a population that prescribes vengeful behavior.194 The effect such a norm has on individual behavior is demonstrated by a study on the example of the antismoking-norm: being surrounded by a large number of punishers facilitates punishment.195 (Observe the similarity to the by-stander effect in Psychology.) An interesting addition is that people sometimes deliberately seek communities with enforcement norms: Alcoholics Anonymous is a fine example,196 where by affiliating to the group one not only volunteers to punish the ‘weak’, but expects his peers to do the same to him. Note that such a norm circumvents the incentive problem for punishment discussed earlier, and also does not necessarily require a special natural inclination to punish. (Like in the case of Strong reciprocity.) The theory of Social Reciprocity also refers to social norms as the motive for punishing anti-social behavior in separate groups. On the other hand, also observe that empirical findings affirm that if an enforcement norm exists, at least in normal circumstances, it will likely be internalized, too. The reason is the evidence for willingness to punish even at a cost and the evidence against multi-level metanorms-systems and strategic punishment. This on the one hand points to that punishment is voluntarily, and on the other hand considering that peer punishment takes place in massive proportions, it is likely to be exercised either out of a natural inclination or because of social norms (instead of self-interest). If we recall another finding presented earlier, namely that norm-driven persons are more willing to punish, then we can see that social norms at least do play a role next to instincts. Thus, peer punishment is likely to be driven at least partly by norms, which must be internalized norms, because this act is voluntary. It also suggests that the primary – the enforced – norm will also likely be internalized, because otherwise one would not adhere willingly to its enforcement norm. 197 (One more note, that a norm is internalized, and a subject is willing to enforce it does not imply the existence of an enforcement norm, which requires that many people do so, and that enforcement be prescribed by a separate norm with some degree of independence.)
1.3.2.5. Role of Social Norms
The next question regarding norms we are going to investigate is their role in society198. Basically, the big question is do norms exist and emerge to serve and through serving an aim or not, and if they do what aims? Trying to find an answer to these questions we encounter two main propositions. Individual functionalists see norms as being directly favorable for the individual. This is the view that would satisfy most economists, as this could solve all incentive problems around norms. As shown above self interest can be defined more narrowly and broadly: from material or social benefits, through norms serving as an excuse or an instrument of signaling199 to interestedness in others’ well-being there is a wide range of possible personal benefits, and some of them are surely involved in norm emergence and
194 Friedman and Singh (2000) 195 Hechter and Opp (2001). 196 Elster (1989) 197 Of course this argumentation is not universally true. Unfortunately, there were many examples in history when people were forced to support doctrinal systems indoctrinate others – an interesting aspect of metanorms. 198 It is instructive to cite here Dasgupta (1993), who have found that in addition to community governance and repeated interaction internalization of social norms is the third important notion by which the literature tries to reconcile the ostensible antagonism between self-interest and pro-social behavior including willingness to punish. 199 See e.g. Posner’s signaling theorem.
- 51 - distribution. Recall that I have already mentioned that internalization is not independent to self-interest. Nevertheless, it is also likely that self-interest is not the only factor here. Collective functionalists 200 put forward that norms are useful primarily to the community. This assumption has some important implications: first, obeying norms can be painful for the individual, second norms are necessarily useful for the society, third there must be a mechanism that propels norms to optimality. Starting from Aristotle many great thinkers have emphasized the importance of social norms.201 An important milestone is Durkheim’s famous notion of anomia, the breakdown of the normative structure of the society, which is an important starting point for collective functionalists as it underlines the power of norms supporting social prosperity. For economists this standpoint means that norms are there to increase efficiency by solving economic problems cheaply, for example by channeling back externalities, alleviating coordination problems and compensating for market failures. 202 Particularly, referring back to enforcement norms, by communities’ ability to locally and informally supervise behavior social norms can greatly reduce monitoring costs. They can also significantly affect criminality.203 More recently, to collect under one term the many facets of social norms’ effect on society, social scientists coined the expression social capital. It includes trust, taking care for others, and norm orientation that is living by them and willingness to enforce them. By today, the importance of social capital 204 is hardly questionable. Although some norms do help mitigating economic life this way, there are others that has nothing to do not only with economy, but improvement of people’s life in general.205 In spite of this, collective functionalists tend to see at least the socially beneficial norms as optimal solutions. How such quality could emerge, though, is a mystery. Now we can see that there are three possible ways to achieve this. First, if individual behavior generated by individual incentives entails global efficiency (like in neoclassical economics, our starting point). Second, by some kind of intentional design (indeed, there are propositions that social norms can be initiated by norm-entrepreneurs, or legal intervention − nevertheless, even if they can when their own laws of dynamics are initiated, intentional forces at maximum can manage them, not control)206. Finally, through some kind of evolutionary process, (but we have seen that evolution does not imply perfection, social evolution even less207). If nothing else, inertia of social norms208 puts their optimality into doubt.
200 Categories of functionalists from Hechter and Opp (2001). 201 Including Thomas Aquinas, Rousseau, Burke and Hobbes 202 Arrow (1971) for example argues that instead of creating incentives that make future cooperation credible, “as an alternative, society may proceed by internalization of these norms [of trust or trustworthiness].” He adds that: “There is a whole set of customs and norms which might be similarly interpreted as agreements to improve the efficiency of the economic system.” 203 Sampson et al. (1997) 204 One renowned work is Putnam (2000). There is also a dedicated webpage to the topic: www.bowlingalone.com 205 And also some norms do not exist, although there are problems that they could solve. 206 We can also mention here the so-called Group Theory, which expects group members to recognize the collective benefits of pro-social behavior and restrict themselves to it. (Recall Team Theory from utopian economists.) Unfortunately, as it is proven day by day, not everybody is so honest. Ostrom (1990) p.5. referencing Betley and Truman. 207 For example because selection is weak and not uniform: heterogeneous agents in all probability use different selection criteria and are influenced by many non-social stimuli from rationality to instincts and randomness. Truly, each of us is differently susceptible to these factors. Another important reason is our great exposure to contingency, especially in the modern world: wars and political events, scientific achievements and technological innovations, and last but not least fashion sweep the globe in a virtually random manner having a great effect on a major part of humanity and interfering with the selection process. There is, however, a possible
- 52 -
1.3.2.6. Enforcement of Social Norms
Most of the time members of the society follow norms voluntarily, but when necessary, social norms are enforced by informal social pressure (in the first place). As we have seen this enforcement mechanism is so important that it is a core element of the definition of social norms. Its significance is further accentuated by experimental and empirical findings showing social norm enforcement can be the primary reason that make players engage in costly punishment. On the other hand people respond to social pressure: they raise their contributions even when no material cost is involved. Others dare to talk with greater generality, asserting that behavior is primarily a product of the perceived judgement of other people.209 In addition to promoting compliance, social pressure also plays a role at the internalization of social norms. Social pressure has two distinguishing characteristics relative to other means of enforcement. The first is the distributed nature of monitoring. As most social actions happen locally, and has only local effects, it would be very difficult to supervise each individual centrally. Instead, agents can watch each other, using locally available information. The second typical feature of social norms is their enforcement. Because of the interrelatedness of norms systems enforcement does not necessarily takes place locally: people can report offenders to a central institution (e.g. the legal authorities) who can take over the cost of punishment. Although some models are based on this approach, in general this method is limited to offences that elicit legal responsibility. The bulk of social enforcement takes place locally and informally,210 which also implies that it is cheap in a material sense. We have already discussed punishments in detail at economic experiments. Much of what has been said there is also applicable to social pressure. There are, however some special characteristics that need to be mentioned here. First just a quick reminder to internal and external punishment: social norms are the most important group of norms that are liable to internalization and subsequent enforcement by guilt. (One note: it is important to distinguish between effects of genuine guilt and public shame. Although fear from both can result in unenforced compliance, the first is an internal and the second is an external motive.) Second, I would like to highlight two kinds of punishment that are special to social pressure. The first is exclusion from a social network, better known as ostracism. The threat of ostracism is a powerful deterrent.211 The reason why it deserves particular attention is that it is another sign showing that the punishment behavior of members in a group can be interconnected. (Remember how most economic experiments control against informal contact and information flow on punishment behavior.) Moreover, this connection seems to be working as a positive feedback. These observations are also supported by another similar effect: lynching. Keep in mind earlier examples also: facilitation of punishment by proximity of other advantage for social evolution: the flexibility of our minds, that we do not necessarily have to wait for generations to pass and go, that we – in principle – can change our minds. 208 Inertia does not stem only from mentality. One remarkable way norms can have a lasting effect on humanity is through their co-evolution with genes, which are of course very hard to trim to swiftly changing circumstances. Another cause is network effects in society. More on this in connection with norm cascades on page - 58 -. 209 Sunstein (1996). Kahan (1997) adds that: “the perception that one’s peers will or will not disapprove exerts a much stronger influence than does the threat of formal sanctions.” 210 Informal is a flexible category. Some call informal enforcement everything that is not legal, but social enforcement also has more (court-like, quasi-institutionalized) and less (gossip) informal means. E.g. in Posner (1996) 211 As shown by Masclet (2001)
- 53 - punishers, but mind also the debate on the by-stander effect. Besides, for a balance, society or communities can utilize positive incentives, too, that is they can reward behavior, as proposed by Esteem Theory212. (The term reward norm213 also appears in the literature.) Either pro- social behavior is rewarded directly, or support can be given to punishers, who consequently might feel a “warm glow” by fulfilling an enforcement norm or by an audience conferring esteem on them. The question if delivering esteem or punishment is costly or not is not settled yet, opinions change from theorem to theorem. The hypothesized cost of rewarding and punishing varies, too. Economists taking the position that they are costly, usually talk about a second order public good214 problem. On the one hand there can be certain material costs, like for example in PG games, but more typical is the psychological tension that one must suffer confronting others. If nothing else, the opportunity cost of the energy and attention spent on acting as a punisher must be considered. 215 Others mention “frowning” 216 or suggest unintentional punishment217 to promote costlessness. Still others bring up the idea that there are people who actually like to punish by nature which is supported by theories of co- evolution of genes and culture. Another group propose that punishers are compensated by sensing a social esteem mentioned above. Social pressure in comparison to other means of enforcement has its own advantages and disadvantages. We mentioned its distributed nature already, which can be a great advantage, but there is another reason why it can be more effective than legal enforcement. The perceived quality of social punishment is fundamentally different from legal means. Especially when it comes to offences related to defending honor, the offender might see corporal punishment, incarceration and monetary fines as an additional price that can be taken. In these cases shaming by the society can more successfully retain him from taking the risk.218 There are, though, certain drawbacks of social pressure. They will be discussed in a separate section.
1.3.2.7. Change of Social Norms
First of all, norms are dynamic entities. There are several examples illustrating this from disappearance of foot binding in China to the sexual revolution in the west. The process by they change show peculiar characteristics both at the individual and the global level. Nevertheless, for a long time, little attention had been paid to their dynamics. (What is more, collective functionalism hypothesized optimality without much reference to how it could come about. Observe its similarity with the static nature of game theory with its equilibrium analysis.) This lack of interest in the origins and development of norms was partly due to inappropriate tools. The growing popularity of evolutionary analysis and the availability of simulation tools, however, changed the situation. In this section I would like to present the relevant factors of norm evolution that should be considered before one starts to write a dynamic model of norms. I do it in a bottom-up fashion: starting with individual transmission mechanisms to the emergence of norms and other characteristic phenomena in norm change.
212 McAdams (1997) 213 Lopez and Luck 214 E.g. in Voss (2001) 215 Elster (1989) 216 McAdams (1997) 217 Horne (2001) 218 Lessig (1996)
- 54 - There are basically two dimensions of norm change: development or emergence – that is forming of norm content − and distribution − spreading of the norm in a population. Let us start with emergence.
1.3.2.7.1. Emergence
There are two things that is sure about emergence of norms. The first is that it is a complex phenomenon, the second is that it is far from being perfectly understood. Naturally, every discipline219 and theory tries to use its own ideas and methodology to capture as much of this process as possible. First of all recall that classical game theory did not have much to say about the appearance of norms. Because of the static nature of its analysis, it mostly treated norm emergence exogenously, and concentrated on equilibrium analysis. Endogenous emergence can only be addressed in an evolutionary framework. Evolutionary scientists see a selection process behind the emergence of norms. Recall the notion of group selection whereby genetic and social evolution walk hand-in-hand. This theory, however can only model long-term evolution that spans time scales appropriate for biological evolution. Short term evolution must have something else in the background.220 As already referred, selecting forces need not to be biological, thus evolutionary models are applicable for short-term norm evolution, too. These forces, however, are much more diverse than biological selection, and models built on them even more: on the one hand their nature is different objectively and on the other hand it is always a subjective decision of the modeler which of them to include and how represent them in his model. We will learn more about the most widely acknowledged cultural selection force, also used in my model: selective imitation, and its variants. Sociology involves a multitude of approaches of which I can talk about the main tendencies. First, it is not surprising that sociologists are the ones who really see the variety of factors appearing in this process. Culture, power, behavioral regularities and other norms221 are all identified as having a substantial impact on norm emergence. (These are basically the “rules of the game” that determine the patterns of interaction or ‘institutions’ as we called them earlier. Their significance is increasingly accepted by the evolutionary movement, too, where it is convenient to speak about a co-evolution of institutions and preferences.222 Note that in Economics where it is not usual to talk about norms, everything is typically approached from an individual point of view. This is why, especially when we are talking about evolution of preferences on a population scale on the short run, it might easily mean spreading of social norms in fact − particularly if we consider the widely recognized fact of how powerful culture is in forming preferences.) Next, there is an important cleavage on the question of which came first: behavioral regularities or the rules that prescribe them. The proponents of the first variant promote that spontaneously appearing correlation of behavior sooner or later becomes tradition, which in turn automatically lends obligatory force to them, transforming mere regularities into
219 For a similarly encompassing survey of mechanisms supporting norms see Axelrod (1997) Ch.7., who lists 7 main factors thought to be important in norm dynamics: metanorms, dominance, internalization, deterrence, social proof, law and reputation. 220 There have been some weird attempts to bend short-term evolution under the umbrella of biological forces, tracking back norm reproduction to biological reproduction. See Lynch (1996). One excellent counter-example is celibacy, which survived for a long time. 221 Hecthter and Opp (2001) 222 Refer back to footnote 122.
- 55 - enforced rules. Those who oppose this view insist on the primacy of rules, that they emerge to with an aim to solve societal problems and then they are imposed on the members of the society. 223 Observe that this distinction reflects the opposition between individual and collective institutionalism since behavioral regularities can be in the first place fostered by individual incentives and achieved through local negotiation without any regard to large scale outcome, while accepting the necessary functionality of norms requires some a priori recognition of the group’s interests. That the first view is based on individual interaction suggests that evolutionary methodology is appropriate for analyzing (short-run) norm emergence, too. Furthermore, sociologists also admit the importance of ‘close-knit’ groups and social networks224. Besides, some propose models with heterogeneous agents, each type playing a different role in norm emergence. 225 Although these models may seem a bit ad hoc, and mostly lack formal analysis, the core idea of interacting heterogeneous agents captures an essential element of real societies that surely cannot be neglected in models of norm emergence. The legal academy of course puts the main emphasis on the connection between the legal and social spheres. Some talks in more general terms, mentioning authority instead of law as a determinant of social norms.226 We will learn more about the expressive function of law and the interrelatedness of norm systems. What I would like to note here is that some legal scholars not only admit the influence of the law on social norms, but assert that law should be designed in a way that considers this secondary effect of it, or rather directly aims at changing norms227. This proposition depicts legislators as ‘change agents’ and it is close to the collective instrumentalist view, and the one that advances the primary role of rules before behavior.
1.3.2.7.2. Distribution
The second main dimension of norm change is its spreading in the population. The general process by which a norm proliferates in a group or society is called diffusion and the event by which individuals acquire norms is transmission. Thus, diffusion is the large-scale outcome of transmission. Transmission can be grasped in different ways. First, by the connection between the donor and the recipient. Along these lines we can identify three basic types of transmission: vertical (norms transmitted from parents to children), oblique (from members of an older generation excluding parents, e.g. teachers) and horizontal (from members of the peer group).228 The personal action behind transmission is imitation. Although imitation and norm transmission are closely related, imitation does not necessarily generate norms: it can take
223 See e.g. in Horne (2001). The first approach is termed sometimes methodological individualism (e.g. by Ellickson (2001a)), while the second is postulated also by Hayek’s functionalism (implying that norms are necessarily beneficial to the society). 224 Putnam (1993) 225 E.g. Ellickson (2001b) for a full blown model. He deploys norm entrepreneurs, opinion leaders and other types of agents each complete with their own behavioral patterns. Sunstein (1996) also brings up norm entrepreneurs who by individual action try to plant norms in society. He also gives some examples. Moreover, he also refers to public interest groups as acting similarly and providing new grounds for pride and shame. 226 Dau-Schmidt (1990) 227 Sunstein (1996) 228 Chong (2000) He terms these the types of cultural transmission.
- 56 - place restricted to isolated individuals, without large-scale consequences. Besides, imitation is a pervasive phenomenon of social life: it also works in connection with fashion, business and tax compliance and even crime229. Imitation is usually not uniform: there is mostly some kind of systematic bias in our choices of examples. This selectivity is interestingly rather skewed: people seem to discriminate more heavily on whom to imitate, than on what to imitate. In other words when we have selected a target person he tends to become and ideal, and we do not care to select what may not be worth in him to copy. Imitation can be a rational act for boundedly rational agents, especially in complex environments, where information is costly and behavior of others can reasonably thought of as a better source of it than independent investigation. Nevertheless, imitation frequently happens unawarely, without conscious reference to self-interest. In fact, we seem to have a genetic predisposition for imitation, as if it has been selected for by biological forces. Considering our personal limitations and the life- style of paleolitic humans where group selection was strong, it is highly possible. In spite of its usefulness, imitation is prone to errors, partly out of misperception, partly from imperfect replication.230 Although this imperfection might seem a flaw in the process, we may see its use recalling from evolutionary studies that variability is a key element of successful adaptation and noticing that variability is fostered by copy errors, just like in genetic evolution. Transmission can be classified by the selection criteria. There is a wide assortment of propositions on how people choose examples, two of them outstand from the rest in terms of popularity: payoff-biased transmission and majority-biased or conformist transmission.231 Both of them are represented in my model. As already hinted imitating successful strategies is readily explained through genetic evolution.232 We only need individual selection and bounded rationality and an instinct of copying successful strategies is easily selected for. In principle, of course, being rational beings we do not necessarily need instincts to tell us to imitate the successful, it can come directly from our rationality. (Nevertheless, our ancestors, in whom the instinct is supposed to have evolved, were governed by instincts much more.) Certainly, imitation gives suboptimal answers in many conditions, sometimes even worse than bounded individual maximization, but being a simple rule applicable in many situations, on average it may be better than anything else. Mind also that imitation is not restricted to individuals. Organizations often copy each other’s strategies, and having no instincts on their own right, they probably do it more out of discretion.233 For conformist transmission it is less clear how it can be connected to rationality or instincts. However, there are at least two signs showing that it could also be supported by biological evolution (which entails that it also has been a rational choice in
229 Kahan (1997) notes that “a person’s beliefs about whether other persons in her situation are paying their taxes plays a much more significant role […] than does the burden of the tax or her perception of the expected punishment” He adds that “social influence on law-breaking has even been confirmed experimentally”, referring to Cialdini el al. (1990) He also accentuates that people tend to imitate respected peers. 230 See Allison (1992) on unaware imitation, selectiveness and errors in imitation. This paper also gives a delineation of imitation from teaching. 231 Other propositions include people are copying agents to whom they are attached to, whose environment is similar, who are in a similar role position, or those who has been in the environment for the longest time, etc… see e.g. Allison (1992) and Horne (2001) Some also raise the possibility of anti-conformism: adopting behavior of a minority. Additionaly, there is an interesting idea called meta-mimetism allowing agents to imitate even rules of imitation. It can be found e.g. in Chavalaris and Bourgine (2003). They also highlight the predominance of the two types of imitation indicated above together with Henrich and Boyd (2001) and Bowles (2003) in its prologue. 232 See e.g. Clark (1989) discussing a biological instinct to conform. 233 See e.g. the behavioral example in Kreps (1990) Ch. 19. Of course the managers’ instincts can also be accounted for.
- 57 - certain situations).234 The first is that mingling in a crowd is still the primary protection for individual members in many species. Secondly, group selection can only work if there are groups on which it can operate (and which also should be small enough to have a common fate). Indeed, humans have lived for quite a long time in such groups.235 Group members, however, have to identify each other, therefore they need to have similar features. Although in some groups it has gone as far as biological differences (typical outlook), cultural and behavioral traits were much more readily available to distinguish between people. Group members must have helped each other more that outsiders, consequently conformity could be selected for. Finally, I would like to recapitulate that imitation is not the only effect that moulds behavior and influences distribution of norms. Our rationality, psychological instincts, frailties and inclination to imitate are all superimposed with the actual environment and work simultaneously in defining actual behavior. How much each of us is susceptible to social pressure is an idiosyncratic feature.
1.3.2.7.3. Norm Cascades and Inertia
There is a very characteristic phenomenon in social norms dynamics. It is the so-called norm cascade, also appearing as ‘tipping process’236, ‘critical mass models’237, ‘snowball effect’238 while others talk about ‘jumps’239 in norm adherence.240 It is basically very similar to the situation that we have found with generalized increasing returns: switching in adherence to a norm by one individual generates an external effect on the rest of the society, because the more people follow the norm, the greater the pressure is to do so. This implies a positive feedback, which results in punctuated equilibria: longer periods of stability separated by sudden changes. The inertia of norms is a widely observable phenomenon: “people sometimes resist cultural changes even when environmental changes undermine the original rationale for their values and actions.” 241 Inertia of social norms, however, has diverse origins: personal features like internalization or habits are only one, but it may have genetic reasons (as hinted under footnote 208) and it has a social aspect coming from the network effect just described.242 Particularly, these sudden changes can also be observed when social norms recede. Our favorite examples, foot-binding and dueling, disappeared in a very short time in comparison to the time span they prevailed. Interestingly, in some situations social norms are swapped in a very special manner: a behavior prescribed by a social norm suddenly
234 Not very surprisingly, payoff-biased transmission is more common in the economic literature. Examples include Carpenter (2002), Carpenter and Matthews (2004), Sethi and Somanathan (1996). Henrich and Boyd (1998), however, show that conformist transmission is superior to both unbiased transmission and individual learning in a variety of circumstances. 235 Encyclopedia Britannica (2004): ”hunting and gathering society” 236 Granovetter (1978). Ellickson (2001) also lists some references to the literature. Picker (1997) presents a computer model demonstrating rapid norm changes. 237 Marwell and Oliver (1993) 238 Hassen (1996) 239 Kahan (1997). He also refers to herd behavior (a similar pattern driven by rationality in the first place) in tax cheating. 240 What I am talking about here is a large scale phenomenon that is these sudden changes happen in the proportion of people following a norm, not within a person. 241 Etzioni (2000) 242 Not specially for social norms, but behavior in general there is another source: trial and error learning: supposing that people are not perfect calculators, gradually accumulating experience their behavior can also improve gradually.
- 58 - becomes prohibited by another.243 This is one explanation for such falls. Another probably less dramatic scenario is when certain norms just cease to be internalized by the majority of people. This undermines enforcement, leading to a growing number of defections signaling to the rest of the people that compliance is not enforced any more, and people having lost their internal motives join in the abandonment. Observe that both kinds feature a positive feedback, only that this force is stronger in the first case.244
1.3.2.8. Limitations of Norms
Although social norms help to solve many societal problems, they also have their downside. There are many reasons why social norms can be inferior to other kinds of control. First, social pressure may be unjust: social norms have no such built-in guarantees like the legal system: for example the punishment can be too severe, or the social rules may not protect outsiders. Second, more generally, there is no guarantee that social rules are optimal, or that they are practiced correctly.245 (At least if we are willing to renounce the necessary functionality of social norms. Accepting social norms’ inherent path dependence, it is clear that sane intentional design can be better than rules formed by historical accidents246.) Third, social rules are frequently elusive, ambiguous, subject to subjective interpretation and − missing formal information channels − hard to learn about. Fourth, group aims can be at odds with a greater community or in other words they can have (negative) external effects outside the group.247
1.3.2.9. Institutions of Enforcement
Although social norms are most often enforced informally, it is not cast in stone that people can not set up certain institutions248 to support them. Indeed, they often do. There are many kinds of possible institutions for example appointing surveillance functionaries,
243 Remember the two categories: prescriptive and proscriptive norms. 244 More on attenuation of norms in Opp (1990). In addition, this kind of behavioral dynamics does not only apply to what we strictly call social norms. Demand for network goods (fax machines, etc…) familiar from Economics and fashion are excellent examples. What is important is the positive externality one’s behavior has on others’ utility drawn from a similar behavior, not the quality of motives or the means of enforcement. It is worthwhile to get a look at the opposing case, too. The so-called positional goods behave just the other way around: owning them incurs a negative externality on other owners, thus demand drops suddenly. This also has societal analogies e.g. membership in exclusive groups, etc… Power also has a similarly peculiar nature: having some power on others automatically lessens others’ power on us. 245 Just think of our favorite examples: dueling and foot binding, not to mention female genital mutilation. Although these (at least the last two) might have some ‘higher aim’ like defining a greater community, this surely could be attained through much more human ways. There is another exotic example in Henrich et al. (2001) a norm that requires people to return favors even unsolicited ones (probably leading to all kinds of strange commotion). 246 Following Posner (1996) 247 Which is not the same as the external effects exerted by a member on another causing the norm cascade. Think for example football-hooliganism, or any kind of sub-cultural defiance to law. (Sometimes the law can be unjust of course. A famous episode in Hungarian history in the 19th century was marked by a strong passive opposition to Habsburg repression, which become a norm, and finally led to a mutually beneficial compromise.) Parochialism and its consequences while clearly detrimental to the wider society, can also be bad for the community itself. 248 I use the word here in a slightly different manner than before, closer to its common meaning and understand a quasi-formal means of norm enforcement.
- 59 - devising a systematic arrangement that facilitates transparency of behavior, applying formal punishment, and ultimately, invoking law.249 These organizational solutions can aim among others at reducing the opportunity of private (out of surveillance) behavior, assign detection to the most effective agents or maximize the cost of being punished250. More generally they try to increase the efficiency of detection or exacerbate the threat of being punished. Setting up institutions require extra effort in organization, therefore there must be a good reason for establishing them.251 The most important circumstances when they are likely to be set up are: when a central institution may have better information on behavior (or contribution), when peers can not punish each other effectively, when people are not sensitive to peer pressure, or when exerting peer punishment is too costly.252 Economists have set up theoretical models to explain the existence of central institutions of norm enforcement.253 Naturally, these models attempted to use selfish motives and individual maximization as usual. Experimental economists, however, observed that predictions derived from theoretical models did not match empirical findings, which suggests that there must be more than individual maximization behind this phenomenon, too.254
1.4. Legal Outlook
The ultimate institution of enforcement in the society is of course law. It is also the most studied, which creates an opportunity to extract important findings of the legal academy that are possibly applicable for other formalistic monitoring solutions as well. Although social norms and the legal system have divorced a long time ago, there are still strong chains connecting them. The sociological wing of Jurisprudence and Legal Sociology are concerned with the philosophical and practical relationship between law and the society. Because of the size and complexity of these areas it would be impossible to cover them in any sense of completeness here; in this chapter we are only able to give a quick look to the history of the sociological thought in law, give some remarks on the discrepancy between the economic and legal standpoint on the certainty-severity of punishment issue and highlight some weaknesses of law, providing us with further ammunition for arguing the relevance of distributed enforcement schemes. Following this, I am going to concentrate on the narrower question of the connection between the law and social norms in the next chapter. We have to examine this
249 A good resource on societal institutions and their capabilities with a rich empirical illustration is Ostrom (1990). Ellickson (1991) looks at the problem from a legal point of view. His findings are similar to Ostrom’s: overemphasized role of formal legal rules in the current curriculum, communities are capable to work out various solutions and optimism about social norms. 250 From Posner (1996) 251 When, by using some kind of central organization, enforcement can be made cheaper there is an arbitrage opportunity that can be exploited by an entrepreneur. (If other circumstances allow for it, too, e.g. legal enforcement is obstructed for some reason, etc…) Dixit (2004) refers to the Mafia as an institution of this kind. 252 Kosfeld and Riedl (2004) 253 Recall how transaction cost economics led to a new explanation for the birth of the firm. Then organizing activity within one firm was proven to be more efficient than engaging in costly transactions between smaller units. Basically, we face a similar problem here. 254 Theoretical models can be find in E.g. Dixit (2004) and Okada (1993) and (1997). Kosfeld and Riedl (2004) refer to the latter two works and show experimentally that they fail to match real-world behavior. The relevant findings are that “voluntary implementation of centralized punishment institutions may represent an important mechanism for solving the free-rider problem in social dilemma games.”, however “the process of implementation is rather complex and therefore it is not unlikely that it fails” but “if the implementation is successful, in most cases the welfare maximizing outcome is realized” even though “the theoretically predicted institution size is much smaller”. It is worthwhile to compare these results with Decker et al. (2003), another experimental study, already summarized above under footnote 72.
- 60 - to get a more accurate picture about social norm dynamics and to see what made me include a representation of central enforcement into my model. In the history of Jurisprudence legal scholars created theories that derived legal rules from as diverse sources as natural principles, divine revelation, the will of a sovereign − and social processes. The sociological school in legal philosophy was formed in the 19th century, when on the one hand development of the natural sciences gave a new hope of a cognizable world, and on the other hand their methodology began to invade social sciences. The advancement in social sciences, in turn, inspired the legal academy to recognize the social aspects of their discipline. Two representatives of the early phases of sociological Jurisprudence are Ehrlich, and his concept of living law, which stands for the “profuse norm- creating activities of the countless associations in which men are involved” and Gierke who emphasized “the importance of the inner life and activities of groups and associations as sources of binding social norms”. Both are bearing a relish of Sociological view on norm creation. Later on, leading figures of the movement, in the first place Pound and Kantorowitz, turned to more practical questions, closing in on Legal Sociology. In the second half of the 20th century, however, the school has begun to gradually lose interest in ad hoc problems and approached other social sciences to initiate an interdisciplinary movement aiming at a complex recognition of “social and economic orders in their complex unity”.255 The two most characteristic features of the school are its positivism − the willingness to reckon with social reality − and its typical view on the legal system − its embeddedness into the society and the continuous interplay between them. This explains also how the traditional concept of the genesis of law (behavioral regularities becoming social norms and finally crystallizing into legal norms) was displaced by a more organic picture, where legal and social norms are intermittently molding each other influenced by many subsystems of the society. There are two aspects to this relationship: the effects of social norms on the law and vice versa. Both faces of this intimate relationship will be analyzed in more detail in the next section. Before turning to it, however, I still have two important issues to touch upon. The first is the legal aspect of a special question that as we have seen economists are also concerned with. This is the problem of whether the certainty or severity of punishment is the more important deterrent factor. Recall that classical economists asserted that using severe punishment with a low probability of detection can be superior to the opposite alternative provided costly detection and costless punishment, and if our primary criterion is social cost. Not very surprisingly, the legal academy − at least the sociological school − holds the opposite position. 256 Considering the relationship between the legal and social normative system it is easy to see why. (See also the coming section.) Without recurring reinforcement from law, social norms are liable to die out, leading to the declination of effective punishment. There are numerous empirical studies providing evidence for this hypothesis.257 My model hopefully will also be able to add to this debate. Finally, it is instructive to see how legal scholars see the shortcomings of law. Probably the most pessimistic line of thought in legal philosophy is legal realism. It advances the contingency of legal decisions, the predominance of non-legal sanctions and the relative
255 Quotations from Encyclopaedia Britannica, the ‘philosophy of law’. 256 E.g. in Salem and Bowers (1970). They argue that law is very remote to most people, which may lead to underestimating the probability of detection in case they violate it. They refer to studies that attempted to provide evidence on the prevalence of severity as dealing with crimes whose detection probability was high anyway, declaring that in fact there is no evidence on that severity plays an important role. 257 E.g. Nagin and Blumstein (1997). See also Ehrlich (1973).
- 61 - unimportance of law. 258 The so-called Old Chicago School occupies a similar position emphasizing the clumsiness and crudeness of legal instruments. It demands that law should retreat from many subsystems of social life, including areas where markets and community governance can supposedly perform better, giving way to the innate regulatory principles of both.259 Jurists of these schools often stress that law can be and many times is flawed, costly to get acquainted with and also to access which makes many people fall back on more traditional ways of regulation260. Other voices warn that legal intervention into social life may lead to further restriction of personal freedom.261 Still others dismiss this issue by expressing a belief in the resistance of culture to conscious intervention. 262 Finally, we can raise everything as a limitation of law that was brought up earlier as an advantage of social norm control: for example it is hard for central authorities to get appropriate local information and many types of central punishment can be accounted for as an additional price that can be paid.
1.5. Interdependence of Norm Systems
The development of the sociological school in jurisprudence, its ideas on social embeddedness of the legal system and a number of other signs mentioned earlier including the tendency of people to conform to authority and sociological observations on how central policy can interfere with local institutions suggest the interrelatedness of the social and legal systems. It is worthwhile to mark this question and examine it separately and in a bit more detail to see why it is indispensable to include a cross effect between social norms and central institutions of enforcement in a model that aims at a realistic simulation of real world associations. In this chapter after mentioning theoretical attempts that aim at separating law and social norms, we examine the possible connections between the two norm systems from two directions: how law affects social norms and vice versa. We emphasize the complementarity between them, and present a legal school that is concerned with their connections and cooperation. Finally we analyze the possible interactions between law and social norms. That there is some kind of connection between these norm systems is hardly deniable to any social scientist. The quality of this connection, however, is subject to debate. It is in the first place lawyers who seek to justify some degree of independence of the legal system, as any kind of uncontrollable, informal influence can easily cast doubt on our faith in the efficiency of law. An implicit assumption for many legal scholars, insulation theory, is an attempt to eliminate social norms’ distorting effect on law. It asserts that although social norms can reduce the effectivity of the legal system, they do it uniformly, without modifying the relative weight of certain legal norms or eliminating the influence of the law completely. Therefore, law has qualitatively the same effect as it would be without social norms, only that it is somewhat weaker. Nevertheless, this position is hardly defendable when one considers the indirect effect that law has on social norms263 and vice versa, described below.
258 Posner (1996) 259 Lessig (1998) 260 Like social norms, community governance and arbitration. 261 Macey (1997). By the way, exploring how to control such a powerful instrument like social norms always involves the danger that someday a tyranny will make use of it. 262 Tushnet (1998) 263 Argued also by Posner (1996). This work is the definitive discussion on governmental intervention into social groups.
- 62 - Let us first examine how law affects social norms. The legal academy has long ago recognized the so-called expressive function of law264, the indirect effect when in addition to sanctioning certain behaviors, the law also stigmatizes them. The classical reference is Durkheim, who claimed that legal sanctions “reinforce and mobilize informal social disapproval”, strengthening the normative climate in the society. 265 Remarkably, even psychologists acknowledge that legislation is able to affect individual mentality. 266 For example there are certain offences, like littering, that would be rather difficult to supervise and sanction centrally. Thus instead, by lending esteem to people who are willing to punish such behaviors privately so that they feel to have the authority of law behind them it still may be possible to enforce them267. To put it another way, social meaning268 of actions can be influenced by the law, and social opprobrium directed towards offenders. 269 Empirical observations are also available to support this hypothesis.270 Moreover, as already indicated, some scholars advance that legislators not only should take into consideration these secondary effects, but they could be able to design law to change social norms themselves. 271 This way law can support, but also try to fight against certain social norms. On the other hand, formal regulation neglecting secondary effects and norm dynamics quite often backfires and subverts useful and well-functioning social institutions and lead to deterioration in control even if it directly aimed at improving it.272 It is usually admitted273, though, that the exact mechanism
264 E.g. in Sunstein (1996). 265 From Salem and Bowers (1970) By today many scholars stress the interconnection between law and other regulatory forces, for an example see e.g. Maher (1998). A typical quotation from Kahan (1997) indicates the relevance of this connection for deterrence: “Punishment does more than impose disutility. It also expresses the community’s moral condemnation”, while Cooter (1996) writes that governments (law) give a moral background for individuals to chastise offenders. The idea, however, is by no means new. We are able to track it back as far back as Aristotle who wrote: “Lawgivers make the citizen good by inculcating habits in them, and this is the aim of every lawgiver.”, (Nicomachean ethics (350 bC)) 266 E.g. in Atkinson el al. (2000) p625. we find: “it is often said that one cannot legislate attitudes. […] But legislation and judical decrees changes public policies and practices, [and] this in turn frequently leads to changes in social norms. To the extent that citizens’ attitudes are serving a social adjustment function, they, too, will change.” Under certain conditions “the quickest way to change hearts and minds is to first change behavior by changing social norms.” 267 Bowles (2003) Ch 14 writes that we should find a way to “devise rules such that […] individuals with other regarding preferences will have opportunities to express their pro-sociality in ways that induce all or most to cooperate.” A couple of further notes are appropriate here concerning the connection of informal sanctioning and the law. Norms of criminal law operate through inflicting sanctions directly in the first place. Nevertheless, there are time to time attempts to expand the range of legislation to offences that are very difficult to monitor and whose legal enforcement is ab ovo hopeless. The explanation of these endeavors is rather that legislators try to reinforce social opprobrium against certain kinds of behavior. (An example is the overly strict Hungarian act on drugs from 1998.) In addition, in some legal systems minor contraventions and offences with a low level of harmfulness to the society may only result in a reprimand from authorities, relying on shame as a deterrent. Moreover, norms of International Law usually lack explicit sanctions. (Of course this is rather a consequence of the chronic lack of instruments to enforce them than an appeal to shame.) See also footnotes 288 and 289 for practical examples where societal pressure is harnessed by law. 268 From Kahan (1997) 269 It instructive to consider how Kahan (1997) sees from a legal perspective the main factors inducing criminality: he lists widespread criminality, low perceived risk of being caught and low stigmatization. (All of these are represented in my model.) 270 Salem and Bowers (1970) for example references a survey made in 1961-62 in US colleges and universities providing evidence on the binary effect of formal sanctions and the importance of the normative climate in suppressing offences. 271 Littering example and intentional design of law to change norms are taken from Sunstein (1996). Dau- Schmidt (1990) also argues for the influence of legal expression on internalization of norms. 272 Suggested by e.g. Opp and Hechter (2001), Posner (1996) and Bowles (2003) Ch. 14, who terms this phenomenon institutional crowding out. He adds that there is a more general danger: extrinsic motives may undermine intrinsic ones, admitting though, that intrinsic motives are often not sufficient, so extrinsic ones are still necessary in many conditions.
- 63 - of predicting this indirect effect that could enable us to exploit societal forces effectively is still missing, which can mainly appropriated to the complexity of the relationship between these norm systems. In contrast, norms also influence many steps of the process of law creation and realization.274 From this colorful palette I would like to highlight in the first place that there are social norms demanding to follow the law as such. 275 This is a crucial point of the connection between norm systems that can greatly enhance their joint efficiency. This idea appears in various forms in the literature. For example some say that it is possible to internalize law276 (which presupposes a moral ingredient in law). Others, nevertheless, state that people (voluntarily) respect the law even if they do not agree with the morality behind it.277 It is quite obvious from history that law needs this backup from social norms, lest it remain pure ink and paper.278 In addition to the mutual influence of the two norm systems, many authors underline their complementary strengths and weaknesses.279 Characteristics of the problems appealing to either norm system can be deduced from their differing aptitudes in monitoring and enforcement. To cut it short, the law seems to be better at solving rare but severe and complicated cases that are costly to punish. Law is usually also more able to control instrumental280 than expressive actions. 281 Besides, central control can be superior in setting focal points in coordination problems, too. On the contrary, social norms could be given greater independence when it comes to monitoring numerous, small defections and where informal punishment can be more effective. That social norms and the legal system are able to complement each other gives a ground for that states should refrain from breaking into well- established local relations without good reason. Instead, where it is possible, and especially in circumstances where the legal morale is low, legislators should try to make use of functioning social institutions and norms, even by transferring resources to local communities282. The complementarity and interdependence of norm systems is the core element of the legal movement called the New Chicago School 283. We have already mentioned the Old Chicago School, a radical branch of sociological jurisprudence, representing the position that law is so flawed in many aspects that it should simply retreat, giving way to self-organizing forces. The New Chicago School, however, is not so pessimistic, and advocates a stance that is fundamentally compatible to the view that can be concluded from the preceding paragraphs. It sees law as closely intertwined with not only social norms, but markets and architecture (all that is externally given in the world), and legal actions should be carried out taking into
273 Posner (1996) and Sunstein (1996) both raise this question. 274 Not to mention the multitude of private and group interests interfering informally with the legal system on a daily basis. 275 Axelrod (1997) Ch. 3 talks about the respect of law. Kelsen’s famous Pure Theory of Law (1942), also presupposes the existence of a hypothetical “basic norm” which lends legitimacy and compulsive power to the whole legal system. 276 Argued by Posner (1997) 277 Tyler (1990) 278 At least where there is no serious repression involved. (See e.g. the failure of the Prohibition.) 279 E.g. Axelrod (1997). Bowles (2003) as described above also see markets, social norms and states as complementing each other. 280 That is the offence is carried out in order to achieve some primary aim, for which to accomplish the subject would be willing to choose another way if it existed. 281 Where the action itself has a special quality that cannot be achieved any other way. Chambliss (1969). Recall the special ability of shaming in preventing offence related to defending honor. 282 In Posner (1996). Economist Dixit (2004) also emphasizes that where law is weak, it should recognize and utilize existing private and communal governance institutions. 283 Lessig (1998)
- 64 - account these complex ties. This school can be seen as the legal analogy of the movements we have met earlier in economics and sociology advocating greater interdisciplinarity in social sciences284: these three subfields seem to be converging to unify legal, societal and economic incentives to harness so far unrevealed synergies. Let us finally examine how diverse interactions are conceivable between the interconnected norm systems in connection with contribution and deterrence. For standard economic theory private and public enforcement are largely interchangeable as far as the costs of the two are the same. However, public deterrence is, as demonstrated, likely to have secondary effects, as any kind of central regulation. Depending on assumptions one might predict a positive, negative, or non-linear response in the strength of social enforcement for increasing central rigor. On the one hand, too effective central enforcement might generate moral hazard, undermining citizens’ vigilance and eventually efficiency of deterrence. On the other hand, too weak public deterrence possibly disrupts social norms and render citizens helpless, which may hinder private action just the same. In addition, how we think about feedback of private deterrence on itself is also greatly a matter of taste: a high level of perceived private deterrence might be a signal about law’s inefficiency (which takes us back to the preceding question), or on the contrary, it might express that the community is determined to fight down crime indicating members willing to punish that they are not alone. Basically, this kind of controversy led me to create such a widely parametrized model. Legislators thus face a wide range of theoretical approaches from which they have to choose before composing the code. First, they can insist on strict economic principles, which often results in enactment of excessively severe and sometimes practically inexecutable legal sanctions.285 Or they can admit the existence of secondary effects, which is, however, only the first step, because then they have to decide on the probable nature of these effects, and a way to exploit them: whether they want to boost private enforcement by simply reducing its cost,286 or they rather endeavor to direct social influence by promoting social norms,287 or just try to leech local information by setting up safe channels for reporting.288 There are many practical examples for such attempts undertaken by central authorities and many of which proved successful.289 To conclude this section I propose that in the light of the complex connections between the legal and social norm systems just demonstrated the recently quite popular notion of co-evolution could reasonably be applied to the relationship of these two big systems as well.
284 Refer back to footnotes 125 and 126. 285 See e.g. Graetz et al. (1986) for examples from US legislation trying to fight back tax evasion. (As I mentioned some legal norms are not even supposed to be enforced legally. They rather express the moral stance of the prevailing government, and then we have a different philosophy in the background.) 286 E.g. Cooter (1998) and Ostrom (1990) p. 205. 287 Dau-Schmidt (1990) 288 An example is www.targetingbenefitfraud.gov.uk, where the Department of Work and Pensions of the UK tries to track down benefit fraud. Another similar site is www.shopthem.com where all kinds of crime can be reported through the internet. A quotation taken from the latter webpage illustrates the success of the scheme: “The site is based on one designed and operated by the New Zealand government which has successfully reported in excess of 250,000 offences in three years and is believed to have saved over £2billion in false claims.” 289 Examples include the usage of shaming in the Far East as an official punishment, attempts at restorative justice in the UK (www.restorativejustice.org.uk) and the fall of New York crime rate since 1993 as a result of the new strategy of the city police to concentrate on order maintenance. (Kahan (1997)). This example is especially compelling when contrasted with the failure of increasing reliance on imprisonment on the national level.
- 65 -
1.6. Methodology
Our round-up would not be complete without discussing the methodology used in the upcoming model in some detail. In this chapter we are going to examine two important pillars my model is built on: agent-based modeling and object oriented (C++) programming, with some extra remarks on Mathematica. In connection with agent-based modeling after giving a definition, we demonstrate the rich ramifications of the method by presenting the many different types of such models. Next we emphasize the intimate connection between agent-based models and the studying of emergent phenomena. In turn we highlight the most important advantages agent-based models offer: enabling experimentation, the possibility to use natural descriptions instead of abstractions, the flexibility of these models, and that in addition to letting experimenters produce comparative statics it also gives us the chance to observe dynamics directly. Finally a number of caveats and criteria for evaluating agent-based models are delivered. For object-oriented programming first we spell out its particular appropriateness for agent-based modeling. Then its two main characteristics, encapsulation and inheritance, are discussed and a few further advantages are mentioned. We close the methodological chapter by highlighting the benefits of Mathematica, the software in which the front-end for the data- generation executable has been developed.
1.6.1. Agent-Based Modeling
First it is instructive to see the definitions of the main subjects of social simulation: the agent and the agent-based model. An agent can be defined as an “autonomous decision- making entity”, many times able to evolve over time. An agent-based model (or multi-agent system) is a system of repetitively interacting agents complete with their rules of interaction.290 There are many types of social simulation.291 I would like to raise four of the main classifications that are crucial to accommodate my model in the simulation world. First we can categorize them by objective. The possible aims of agent-based simulation span from inducing qualitative intuitions to deliver quantitative results that can be used directly in decision-making.292 Models devised for obtaining qualitative insights give us a wealth of data that may contain important clues about the deeper structure and operation of the system of interest, and in turn can inspire new hypotheses. 293 Second, models can be stochastic or deterministic. As emphasized before evolutionary models necessitate some kind of randomness, which is why I am using a stochastic setup. Third, agents can be spatially fixed or mobile, and the topology of the world or the agent array can also vary widely, depending on the social situation or network modeled. 294 My model is not a spatial simulation and because social connections are usually durable, I use a fixed network which, however, can be configured arbitrarily. Finally, many simulations are specialized to agent, functional or
290 Following Bonabeau (2002). There are other definitions, but these elements are more or less common to all. 291 Gilbert and Troitzsch (1999) is a nice introduction to social simulation and its ramifications. 292 Bonabeau (2002). 293 Bowles (2003) 294 See page - 45 -.
- 66 - network complexity295 in the first place, while keeping the rest of the model at a relatively basic level. It is one of the main strengths of my model, that it allows the modeler to choose the degree of complexity for each, and compare the different specifications.
I have already mentioned296 that making predictions can be extremely difficult in a special form of dynamic systems: with a large number of interacting agents. Many times even the most sophisticated analytical methods are doomed, despite the actual rules that govern the behavior of the nodes can be extremely simple297. Sometimes, although in these systems all interaction happens locally, large scale phenomenon emerge, called emergent phenomena, marking the history of the system as a whole. Quite often even statistical methods fall short to give us a good prediction, because – depending on the nature of the interaction – individual effects do not necessarily average out, and small fluctuations can be amplified over time. In these cases, even in perfectly deterministic models, we have no other choice but relying on simulations and actually carrying out the computations through a large number of iterations: agent-based simulation is the canonical tool for exploring emergent phenomena. There are many, otherwise rather different areas in science where this kind of unpredictability raises a considerable obstacle, for example cellular automata, financial markets, weather forecasting, and so on. Social networks also subsume to the above definition: in society we have a large number of agents who are influencing each other, only this time even the rules are not so simple. We also witness emergent phenomena in social and economic life day by day: sudden bears and bulls in stock exchange prices, inflation and economic cycles, panicking crowds and revolutions, fashion and social norm dynamics: there is an endless list of unpredictable phenomena stemming from the very pattern of social interaction. Thus, the first important sign when one should consider using agent-based simulation as a primary tool of analysis is the presence of possible emergent phenomena. When are chances for that? The most essential sign are:298
● Non-linear interaction299 ● Behavior exhibits memory, Path dependence, Adaptation300 ● Heterogenous agents or interactions, Network effects
The situation modeled herein features most of the above. There are, however, a few other reasons for using simulations in social sciences. We have mentioned one of them earlier: that it enables us to do experiments that in the real world would not be feasible for various reasons.301 Moreover, it enables us, to try out and compare the consequences of many assumptions about human agents and their interaction. This is
295 Agent complexity stands for the complexity of modeled cognitive or mental processes. Functional complexity is when there are many types to agents interacting in a system simultaneously. Network complexity denotes the convolution of the connections between nodes. From Zheng (2002). 296 In footnote 113. 297 The classical example is probably the most renowned cellular automaton, Conway’s Game of Life (Scientific American (October, 1970)) for which given an initial setup and the rules there is no way to tell directly what the state of the system will be n turns away. 298 From Gilbert and Conte (1995) and Bonabeau (2002). The latter also adds hysteresis, non-markovian behavior and temporal correlation. 299 Cp. Axelrod (1997) Ch. 3., who emphasizes that “the evolutionary approach is inherently probabilistic and invloves non-linear effects”. 300 Edwards et al. (2003) highlight that using imitation makes a model naturally individual-based. 301 See page - 45 -, in connection with social networks. Many of what has been presented there are also relevant to agent based simulations.
- 67 - particularly useful since, as we have seen, in the present state of the discipline uncertainty about economic behavior is just increasing. On the other hand, there are many voices stressing that simulation seems to be the only viable method for grasping realistic social setups, because not only their mechanisms are uncertain, but they are also too complex also for obtaining analytical solutions.302 The second typical sign that indicates that simulation can be more successful than analytical methods is when a natural description of the system is available that is we are able to describe individual agents and their interactions directly. Then we can avoid dealing with artificial abstractions303 that by definition ignore many subtleties of reality and are apt to produce results prone to artifacts. Network effects, complex and stochastic individual behavior are especially susceptible to call in for agent-based simulation. 304 Alternatively, these abstraction or aggregates can be computed from the simulated data, and compared with the analytical findings. 305 Furthermore, it is often even easier to examine parts and their behavior than getting information about highly abstract general indicators. Beyond the compelling reasons that make agent based simulation necessary, it has some further advantages. Firstly, it is relatively easy to implement and running models are flexibly modifiable and extendable. It is especially true for my tool, where the rich parametrization allows for trying out and comparing a wide range of theoretical models just by tweaking a few parameters. This takes us to the second advantage: experimentation. One of the main drawbacks of social sciences as opposed to natural sciences is that experimentation is very limited either by ethical, material or practical reasons. Agent-based modeling offers an escape route, making “in-vitro” examination and usage or generation of hypothetical data possible. It can also save money when we have to decide on large-scale investments into complex processes.306 Next, simulations are excellent for exploring dynamic systems, as we can literally see and control every detail of their changes − and as presented explicit dynamics is a core element of evolutionary models.307 For social simulation this implies that the social learning process, spreading of different strategies and behavioral patterns can be ‘caught in the act’. In our special context it means that we can examine the diffusion of social norms along with the evolution of individual agents. Finally, agent based simulations in general, but my tool is especially good for producing comparative statics308, which seems to be on short supply in empirical studies.309
302 Bonabeau (2002) writes that “any realistic situation is likely to lie beyond the grasp of [game] theory”. Axelrod (1997) qualifies agent based methods the “only way forward”, and Stoker et al. (2002) says that computer simulation is “often the only way to investigate dynamic consequences of social theories”. 303 Like representative agents, aggregate functions, etc… 304 Also from Bonabeau (2002) 305 We must mention that mostly aggregates are the focus of interest. Agent-based simulation is also used to see how aggregates build up from local rules and interaction. See e.g. Edwards et al. (2003) comparing an agent- based model with its mean-field approximation. He also confers references to other works showing that outcomes may differ. 306 Simulation is widely used in practice, too. Bonabeau (2002) reports examples where firms like PWC and Ernst and Young used agent-based models in business situations and risk assessment, and predicts further upsurge. Various industries also use it, one example being the so-called queuing models to assess throughput in various systems with alternative arrangement of their elements. More on it in Law and Kelton (2000). (Even though it focuses on industrial application, one can learn a lot about the technical side of simulations from this book.) 307 Bowles (2003) Ch. 14. 308 An example is Carpenter (2004a) who examines the effects of changes in group size with a simulated model. 309 E.g. Carpenter (2004b) draws attention to this fact. Decker et al. (2003) also emphasizes that experimental results might be sensitive to the experimental design.
- 68 - As real world experiments are costly, simulations can be a valuable tool to suggest what cases would be worth a closer look in reality. For example, we may try to find out more about the robustness of the effects of different punishment schemes to variations in many parameters of the model − and the corresponding alterations of real-world circumstances. We should mention the criteria by which simulated models can be judged. They are basically the same as with analytical models: the model should be based on real-world phenomena with sufficient empirical validity (in most cases this goes beyond what is expected from analytical models), and to be able to deliver testable predictions. There are a few special caveats that should be kept an eye on. Simulation methods can bring in special artifacts into the result. First, certain types of iterated dynamics can be very sensitive to the initial conditions as small differences can be amplified by the process. Second, for the same reason even with today’s high precision computers rounding noise can lead to significant alterations from the ‘real’ process.310 Third, the quality of pseudo-random numbers used in stochastic models is crucial: for example it is easy to conceive that a bias in the mean can very easily lead to false conclusions. Fourth, to be sure that we have valid results, it is essential to run our stochastic simulations more than once with different random seeds, lest the output be an artifact of the special random sequence we used. This, consequently, most of the time necessitates some statistical analysis of the results.311 Fifth, when making comparative statics that is when we are concerned with the effect of parameter changes on the final output, (and lacking capacity for multiple runs with the same parameters) we often use the method of common random numbers (i.e. using the same seed in different runs with different parameters) to be sure that the effect of using different random sequences does not interfere with the change generated by the modification of the parameters.
1.6.2. Object-Oriented Programming
The object oriented approach312 in programming has a great intuitive appeal for social simulation. First of all many objects of the real social world, as well as agents of our models can be interpreted as instances of a class: we are all people, with different personalities, just like our simulated agents can be instantiated from the same class but be given idiosyncratic characteristics by setting different member variables and parameters independently for each of them. Furthermore, we can define objects using collections of agents and groups as their members and handle them with similar ease: internal functionality of these super-objects representing the rules of interaction between the agents. Encapsulation is the first of the two main principles of object-oriented languages. It means that each class is a self-contained entity, complete with its own functionality and data content communicating with other classes through a standardized interface. This interface is the only link to other classes: when implementing a new class we do not need to care about the inner workings of other classes, we only need to know this interface to use them. This makes these languages ideal for modular programming. For example we can freely vary the rules of interaction between agents without having to be concerned with their internal functionality.
310 Hints on these (and many other fascinating things about chaos and fractals) in Peitgen et al. (1992). 311 Law and Kelton (2000) 312 Some ideas for this section from Zheng (2002)
- 69 - Inheritance 313 is the second basic concept. It stands for the ability that allows for defining new classes by specifying how they differ from other classes. This way we are able to carry out model development incrementally and flexibly: first we define a basic agent, then its class can be extended and modified by inheriting new classes from it investing our agent with new traits without having to bother about the functionality that is already implemented. This is also an excellent way for creating heterogeneous populations, where agents have a common behavioral core, which can be modified differently for different types. Moreover C++, the language in which the data-generation part of my model is created, is a very flexible tool. One the one hand for its portability the same source code can be compiled to run on various systems. On the other hand it gives maximal freedom for the programmer, without the limitations of specialized languages or packages. In addition, it builds very fast executables whose value cannot be overemphasized, especially when one also wants to produce datasets that allow for statistical inference. With all advantages of C++, it is still a low-level language, which is why data analysis and graphical representation would be rather clumsy to do with it. Fortunately, high level languages designed exactly for this purpose are available and can be linked with external programs. I have chosen Mathematica as a front-end to the simulation part written in C++. Mathematica has excellent capabilities for data analysis and manipulation, it can produce outstanding graphical representations while at the same time it is a high-level programming language as well and is able to control external executables with ease and simplicity.314
1.7. Summary
By now we have everything in our hands that is needed to set up our agent-based model of pro-social behavior. To facilitate understanding its structure and see how it follows from the literature, I provide a short overview of the material we have come through, and give a brief summary of the most important lessons drawn from the interdisciplinary study, the corner-stones which the upcoming model is built on.
1.7.1. Roadmap
We have seen how Economics built a crystal tower on the unerring, selfish and atomized image of Homo Economicus. We have observed how the neoclassical school defended itself against the menace of externalities and the public good problem. We have witnessed how certain phenomena missing a solid explanation in the orthodox framework became enlightened by dropping some of the restrictions on economic man. We have considered how movements bold enough to reexamine the old tenets gained momentum and demonstrated numerous phenomena still regarded anomalous to the axioms preserved from
313 The two principles are from Chapman (1998). 314 The Mathematica front end performs the following main tasks: firstly, it sends the (global) parameters to the simulation. Parameters can be programmed: for example there are routines to automatically run the simulation over parameter grids of arbitrary dimensions. Moreover, thanks to Mathematica’s capability to manipulate text files, it is also able to handle complicated projects with agent and network heterogeneity. Secondly, it loads the exported raw data, computes various statistics from them, and produces different graphs and figures to facilitate data analysis. It is important to highlight that the Mathematica part has very little specificity to the present project, and could be quickly modified to accommodate completely different projects.
- 70 - the original set. We have reflected on how new theoretical approaches developed to involve learning, evolution and social ties as promising candidates for a new paradigm which hopefully will able to grant us with new tools and a better explanation of our dynamic socio- economic world. Then, turning to Psychology, we have got a first hand look at our minds, the origin of all human actions and an indispensable subject of investigation for anyone into building a model with realistic agents. We have regarded the most essential elements of different schools approaching human minds with their own philosophy. Then we have learnt about the basic factors generating individual differences and a heterogeneous society, followed by a short excursion into social psychology to get a more direct insight into human interaction. Next, we have explored Sociology’s terrain, and get acquainted with social networks and social norms, fundamental elements of societal interaction, occasionally referred but seldom examined directly by newer economic models. This is why we have spent some time studying norms’ birth, distribution and effects. In turn, we wandered into the legal academy to behold how jurists got infected by similar ideas as certain economists and sociologists arguing the need for a complex treatment. Finally, we have familiarized ourselves with the most important methodological principles and practice to acquire a quick overview on the technical side of our investigation.
1.7.2. Lessons
Neoclassical Economics was built on the idea that restricting socio-economic behavior to be governed exclusively by selfish motives, perfect information and stone-cold rationality can successfully describe and predict human actions as far as material costs and benefits are concerned. There has been some doubt on it from the beginning, but the clarity of axioms, the “scientifically quantitative” methodology and elegant theorems it allowed for seemed to be such a great prize that it successfully held the discipline back from departures towards new directions despite the growing evidence against the basic axioms’ universal validity. Nowadays, finally, this evidence is considered more and more seriously, and the resulting advances promise to enable us to handle many economic situations more realistically. In the meantime, other social sciences explored the complexity of cooperative behavior, its individual and societal aspects and so, fortunately, now we can use this knowledge by incorporating it into our formal models.
1.7.2.1. Multiplicity of Behavioral Patterns
One of the most important conclusions we can draw upon our review is that human beings are not strictly strategic creatures, many times even when circumstances would favor it. Although rationality is undeniably a strong component of our mentality, it is far from being the only one. It is accompanied by imitation and conformism which in particular situations, in the first place amongst highly complex environments can be interpreted as just a feasible form of rationality, but in many aspects the two mechanisms markedly differ from each other. In many social settings instead of rational calculation people tend to use sampling, either the typical or the successful, and do it even when sobriety would dictate otherwise. While imitation already can be perceived as a lower level of cognition, our minds have inherited even simpler and more straightforward mechanisms that constitute the leading force of animal
- 71 - behavior. Conditioning or at least very similar direct effects have been recognized in action even in economic experiments. In addition to these characteristic determinants of behavior, people are exposed to a myriad fainter, immeasurable and haphazard influence from their environment, plus they are proverbially liable to err, which brings in a noise into their behavior. Although noise sounds like an imperfection, it may play an important role in evolution.
1.7.2.2. Free-riding – Central and Local Enforcement
Neoclassical tenets directly imply that people are not willing to act in any way that − at least in expected value − does not increase their own utility. To our present knowledge this is not true, at least not universally true. The presence of motivations other than rationality in behavior is already a hint on our partial independence from blatant selfishness and individualism. Moreover, recent experiments have provided overwhelming direct evidence on people’s willingness to act for normative reasons, supporting common welfare, more specially to punish even when it is costly and even when there is no hope of future recovery either for the punisher or any other person in whose welfare the punisher might be interested in. This willingness, though, is different from person to person and also it is not independent of the actual circumstances, amongst others the burden it implies on behalf of the imposer, and most probably the general level of morality in the group. The other side of the coin is that defectors tend to react to punishment the way they are supposed to − either because they are aware of the expected slump of their material well-being or because they want to avoid pain and shame. Decentralized enforcement of public rules, however, is not a universal solution, right because it depends on circumstances so much. Although community governance often assists even supersedes formal rules and institutionalized authorities, it has its own limitations. Central enforcement and governance can prove to be a better solution, for example, when it comes to coordination problems, general and formalized rules and costly punishment. Nevertheless, it also has its weaknesses at certain points where local enforcement seems to better fit the problems. Principally, where a large amount of local information is necessary for keeping order and where formal punishment has low deterring power, central institutions should give way to alternative means. Systems of enforcement living next to each other do also interact, which is why policymakers should always consider not only the direct but the secondary effects of their interventions, otherwise even schemes devised with due care can easily backfire. For an efficient functionality of society the complementary capabilities of different enforcement regimes should be utilized, and their influence on each other considered.
1.7.2.3. Adaptation and Networks
As Psychology recognized, Sociology reinforced and Economics slowly admits, people are adaptive that is, in economic terms, even their preferences can shift from time to time based on past experience. Adaptation in general means adjustment to the environment, and one of the most important parts of a person’s environment is social environment: people are ready to receive social influence. Adaptation, together with genetic diversity, is also an important factor making people different. The reason is that the basic aspects of personality
- 72 - evolve in early ages and because this adaptation takes place in different environments. This also shows that some elements of the personality are more resistant to environmental influence than others. Nevertheless, all behavioral characteristics are subject to some degree of inertia, mainly because of different levels of susceptivity and exposition to external impulses. On the other hand, people are connected in social networks, entailing that they have also the means to transmit their stimuli. A social network is radically different from the emblematic institution of Neoclassical Economics, the market, because its structure is not universal, and the actual structure is able to strongly affect economic outcomes by determining who is connected to whom, who can influence whom, how and how fast information can spread in the population. The consequences of micro-level interaction and behavioral adaptation through social networks, in turn, may easily become visible at large- scale, inducing economic breakdowns and manifesting in shifting social norms. A social norm is not simply the sum of individual behaviors. Its most important characteristic is that it is also enforced in some informal way, either through external peer pressure and punishment or internal morality and conscience. Owing to this enforcement mechanism and also the inertia of individual behavior, social norms are sometimes reluctant to change, but they are far from being fixed. They have their special dynamic properties and when they change they tend to display typical patterns, for example norm cascades.
1.7.2.4. Evolution of Behavior
Even the original, perfectly selfish and unerring Homo Economicus can change its choices in response to changing circumstances. Without some degree of responsiveness every organism dependent on a variable environment is sentenced to death. The question is how deep these changes are and how they come about. The Neoclassical view shields underlying preferences and the perfection of maximization. Classical Game Theory holds on to this, but by allowing for strategic interaction new factors appear to be considered when deciding about optimal strategies. Information economics gives up perfect information but actors can still use the available information perfectly. Bounded rationality appears in Transaction Cost Economics but it still keeps from questioning maximization as the cognitive background of behavior. Evolutionary Economics has been the first to take the bold step that leads from maximization to adaptation, from cognition to behavior. Behavioral models concentrate on behavior directly, without requiring strict assumptions regarding the underlying cognitive processes. This, at the same time, facilitates insertion of a deeper level of adaptation into our models, resulting in an evolution of behavior. Evolution and its models are various. The basic idea of evolution, familiar from biology, operates on individuals. This, however, is not the only way blind forces of selection can lead to a more perfect adaptation. Firstly, whole groups of individuals exposed to external competition and similar conditions may co-adapt, recalling the idea of group-selection. Secondly, individuals themselves may change, most importantly adapt, during their lifetime. This has little relevance for biological evolution as for these changes to have an effect on the macro-scale stringent requirements must be met. Most importantly acquired features must be somehow transmittable: either genetically or culturally. Animals normally do not have a culture − humans usually have, making us capable to a non-genetic kind of evolution: social evolution, which can greatly influence behavior both at an individual and social level. Thirdly, looking at social evolution from another aspect we can define it as an evolution of ideas,
- 73 - memes or norms instead of individuals. Because of its relevance, social sciences must consider social evolution when approaching behavior of human populations.
1.7.2.5. Simulations and Experiments
Luckily, by today Economics has begun to breed many kinds of evolutionary and behavioral models. Taking behavior as the basis of formal models jeopardizes the old ways of Economics, not only because we must update our conclusions, but also because much of our analytical methodology has been perfected to solve problems where maximization is the key element. The behavioral approach does not only requires new ideas in describing economic actors, but new technical approaches which is able to handle complex, irregular and organic systems with often chaotic dynamics and emergent phenomena. This hauls Economics that used to be approaching a status of theoretic science towards an experimental one, experiments being carried out in either real life or through computer simulations of agent-based models. There is another sense in which the new approach is experimental: we have lost our last fix point with the abandonment of maximization, so we must begin experimenting again with new mechanisms. In this sense even analytical models of Evolutionary Economics can be termed “experimental”.
1.7.3. The Way Ahead
Although economists realizing the viability of the new ideas might feel a bit being expelled from their crystal palace back into the jungle around it, we must not forget that this uncontrolled and quite often dazzlingly complicated natural place with its imperfect rules and entangled interactions is the primary focus of our interest. What kinds of models give us the right answers of course depends upon what kind of questions we pose. Simple old models of uni-dimensional minds315 can be still useful when we face uni-dimensional problems where one particular quality of our minds gets the upper hand on the rest. Nevertheless, in most situations of our lives ambitions, motivations and influences of the most diverse kinds are inseparably intermingled. 316 The situation is similar with models of aggregate or average behavior and representative agents: in many situations this is still an acceptable approximation that renders further complications superfluous, but when we are aware of the presence of agent or network heterogeneity, we should look farther. In such cases, when the situation is clearly outside the grasp of particularistic theories, trying to force their recommendations probably do more damage than good.317 On the other hand, scholars of the
315 This expression comes from Caldas and Cohelo (1999) refering to the phenomenon that each discipline tends to emphasize one special quality of human beings. 316 Three references expressing a similar view follow. Firstly, Elster (1989) writes that „actions typically are influenced both by rationaliy and by norms [and] sometimes, the outcome is a compromise.” (Observe that he is talking about multiple motives working inside a person.) The other source (Cullis and Lewis (1997) concretizes it to tax payment (a case of the contribution phenomena) referring back to another model and identifying distinct types of agents (Compliers, Identifiers and Internalizers) with different motives. My model is able to handle both situations. The third paper is Chavalaris and Bourgine (2003) which talks about imitation as “competing and completing” rational choice. 317 Bowles (2003) Ch. 14 for instance warns that in a world predominated by incomplete contracts pursuing ideal markets regardless can even more exacerbate the market failure. We should also remember that there are two possible reasons that call for new theories: firstly, that old theories could be faulty originally, and secondly the world could have changed in the meantime (as opposed to natural sciences). Bowles also emphasizes the
- 74 - new complex approach usually agree that as diverse the problems might be, so diverse the repertoire of solutions is.318 Being aware at last of the spectrum of possibilities, we need not restrict ourselves to the instruments of one or another discipline any more. This, of course, further complicates the therapy, for we have to reason for our choices even at the level of axioms somehow, which, overwhelmed by such a complexity depicted above is not easy to put it mild. I hope that I manage to create a tool that might be of a little help in the quest for future theories and policies.
transformation of the economic system leading to a greater prevalence of increasing returns and other phenomena that some time ago could be dismissed as marginal, but today have a substantial hold on economic processes. Instead of trying to find a way that allow us to see reality the way we would like to see it, we should always be ready to modify our assumptions and models when necessary to make them more empirically grounded. It is hardly use to wrench old theories until we can somehow push reality under it. For example, if you recall infinite regress in metanorms, that is a typical example for this kind of futility. The aim should not be that we defend outdated paradigms, but to understand reality using all the opportunities we have. (My thoughts parallel Kreps’ (1990) argumentation in defense of the behavioral approach (p738) against believers of the neoclassical model.) 318 See e.g. p11 in Ostrom (2001): “I argue that many solutions exist to cope with many different problems”, adding (p216) that current models overemphasize central solutions and also making particular note (on p18) that there can be many ways of enforcement. Consider further how economists talk about the question. Decker et al. (2004) admits that “generally optimal punishment rule may not exist”. Bowles and Gintis (2000) stand up for a more interdisciplinary approach in Economics and Bowles (2003) Ch. 14 for a complementary treatment of markets, communities and states as regulatory forces of economic action, as noted before. Also notice the legal recognition of the fact that there can be a variety of personal and social motivations behind criminality (e.g. Kahan (1997)), which also means that the cure is likely to be different as well.
- 75 -
2.Part II
Models
- 76 - This part incorporates an enumeration of the most closely related models to Contributron that can be found in the literature, the detailed description of my model and a few special highlights on certain aspects and elements of it.
2.1. Related Models
Before getting to describe my experimental tool, I would like to introduce some other models that inspired or are otherwise related to my present effort. There are two models connected more closely involving that I have borrowed some of their elements to transplant them into Contributron, and number of other works that are associated less tightly. The model that inspired my work most directly can be found in the third chapter of Axelrod’s 1997 book, “The Complexity of Cooperation”. The title of the chapter is “Promoting Norms”. It contains an agent-based model that was built to explore how willingness to punish and shirk changes in a society governed by differential replication (that is where the more successful agents had more offspring). The two parameters featured in my work ‘Boldness’ and ‘Watchfulness’ (under the name of ‘Vengefulness’ 319 ) with the probabilistic treatment of norm-adherence come from this model. It has also shown that the contribution-punishment puzzle is closely connected to social norms, and that it is fit for the evolutionary approach using agent-based methods. It also suggested that the problem is well worth further efforts. In hindsight at least, his findings were not very surprising. Starting from random initial conditions his basic model produced final output in which he could detect three different clusters: high average Boldness with virtually zero average Vengefulness, a moderate level of both, and high Vengefulness with low Boldness. Basically this means that high levels of both simultaneously can not survive for long. (Which is quite intuitive, considering also that punishing was costly to the punisher, too.) In the same chapter he tested an extended version of the model, where he added metanorms, allowing agents to punish those who have not punished defection. It, certainly, boosted both cooperation and ‘Vengefulness’ and suppressed ‘Boldness’ in the results. This model, however, is different in many ways, from what I am going to present here. Most importantly, it is a traditional, specialized and ‘amalgamated’ model, like most in the literature. It was created for examining one strictly narrowed down situation with one special set of assumptions − with no intention for further extension or wider exploration. It featured a special social net, all agents were connected to everybody else, and the only force moving strategies was success. My tool, in contrast, has a different philosophy. It aims at being able to incorporate many such models from which the experimenter can choose, and compare the results. For example my agents feature rationality, social sense and psychological reactions as driving forces, from which any arbitrary combinations of behavioral motivations can be mixed together by the experimenter (if needed, for each agent separately). The structure of the social network is also arbitrary, letting the experimenter explore quickly how difference in structural setup may affect results in different circumstances. Furthermore, my model is also open source so that anyone with sufficient enthusiasm can extend it with elements not hard- coded already.
319 It also works slightly differently in his model, because in order that an agent can punish, he also need to ‘spot’ defection, whose probability is measured by another parameter. In my view there is no real need for such distinctions as the two can be combined into one parameter without any loss of generality.
- 77 - Another model that gave me inspiration is Kosfeld and Huck (1998) and its follow-up from 2004. Although it is an analytical model, it is concerned with similar problems, and has some common elements with my work. In their first work they implement a model of a decentralized enforcement scheme where agents could monitor each other and report defection in bilateral prisoner’s dilemma games to a central authority which actually punished the shirkers. (This one is important, because this makes it possible for them to arrive at policy recommendations, as for them the central authority decides on the strength of the private punishment. In my model this relationship is more subtle.) One of the common elements with my work is that the two types of behavior agents could exert (defecting and reporting) was governed by different forces (unlike e.g. in Axelrod’s model, where both change by yielding to success). For Kosfeld and Huck strategy in the PD game was outcome oriented, while the monitoring activity, though also dynamic, moved due to the so-called ‘socialization by control’: one was more susceptible to become a monitor when he was actually punished by someone else than when only deterred. (There is a similar effect in my model: seeing punishment can alter ‘Watchfulness’ directly.) Another element that I have adopted slightly adapted is their steady drift that drove agents from being monitor types. 320 Their results showed that local control can be a sustainable source of enforcement and it can produce a large degree of cooperation even at relatively low levels of socialization. They also found, though, the possibility of a policy trap, where more punishment induces less cooperation. (Basically because when there were too few defectors, without the stronger influx to the punishing group from the actually punished, punishers could die out.) Then they called out for legislators to pay attention to the possible indirect effects that law may exert on society − a position largely in accordance with the notion of expressive function of law presented above. (Such effects are also included in my model.) In the 2004 sequel to the original paper they applied their model to the neighborhood-watch program, and ended up with similar results. There are a couple of other models related to my work more loosely. I have already referred Kandori (1992) 321 , who uses a game theoretic model to show that community enforcement can be more effective than individual.322 He also examines the possibility of selective enforcement by local information processing, when shirkers can be punished without hurting others − similarly to my model − because they carry a label of their type. With his special assumptions about strategies followed by guilty and innocent players and rules about revising agents’ labels (guilty agents can be ‘forgiven’) he obtains that the community is able to realize any mutually beneficial outcomes (i.e. the Folk Theorem). There are many models concerned with survival of pro-social behavior and proportional changes of different types of agents (free riders, punishers, etc…) in a population.323 What should be noted about them is that − as indicated above − unlike in my model agents in these ones usually have fixed contribution and punishment properties 324 whose population penetration are jointly governed by rules of differential replication that is by success. They, however, aim at long term evolution and biological selection, whereas mine has more to do with short term processes where selecting forces are mostly social and psychological, and, as we have seen, much more diverse than narrowly defined self-interest.
320 In their second paper they even propose a second drift which could be fostered by the government. This resembles to the direct effect on W in my model. 321 Under footnote 47. 322 Recall the corresponding experimental results presented in Carpenter (2004a) and Decker (2003) described under footnote 72. 323 Bowles and Gintis (2003) is an agent-based example, while Carpenter and Matthews (2004) and Sethi and Somanathan (1996) use an evolutionary game theoretic model with the above features. 324 E.g. there is a type who contributes but not punishes, another that does both, etc…
- 78 - Indeed, there are models also of interest containing other than selfish motivations, accentuating the theoretical relevance of social factors.325 Many works could be used to compare particular results from my model run with different settings. For example numerous theoretical models are devoted to find optimal policies for taxation.326 They can be a benchmark as my model can also be used to examine such problems. Carpenter (2004a) can also be interesting because it uses simulation to assess the effect of changes in group size on peer monitoring, which is very easily reproduced with my model. Of course, comparison with empirical findings is also essential. Many of the works quoted earlier, and especially those presenting experimental results provide an opportunity for this. Finally, there are many models using similar techniques and ideas supporting particular parts in my model. They are referenced at the discussion of the respective elements.
2.2. The Contributron©
The Contributron is an agent based modeling tool. I must underline that this is not a “conventional” model that can be found in most papers using the agent-based methodology. It has been designed to include the most general mechanisms discovered to govern human behavior in connection with cooperation, contribution to common goals, free-riding and punishment. It is not intended to push the idea that agents are governed by the implemented mechanisms or any of their combinations in general or any particular form of the contribution-punishment phenomena. But it is intended to let experimenters observe how different assumptions on social context and human behavior alter the dynamics of a system of interconnected agents and the final outcome. Its wide parametrization aims at this end: experimenters are free to eliminate any effects by setting the control parameters to zero, or choose any mix of their interest with maximal freedom and flexibility both for agent behavior and social structure. The implementation allows for producing comparative statics and analysis of dynamic data as well. Due to its modular, object-oriented implementation and the open source code, both the data generation part and the Mathematica interface are readily modifiable and extendable. In this chapter after a short informal introduction to the most important hallmarks, I am going to give a detailed description of the tool.
2.2.1. Hallmarks
Contributron is an attempt at synthesizing the findings of a thorough literature review summarized in the first part covering many aspects of human cooperation. The most important features of the model are:
● Agent behavior is described in two dimensions: willingness to contribute and willingness to punish defectors. Each agent has two associated variables determining his behavior in both dimensions. The value of these variables can be interpreted as adherence to two social norms: the first requiring agents to
325 For example Myles and Naylor (1996) use a social custom and social conformity source of utility, Margolis (1991) employs individual and social preferences, and Henrich and Boyd (2001) examine how selfish and conformist transmission can be combined. 326 Referenced under footnote 30.
- 79 - cooperate and the second to enforce cooperation in their neighborhood. The distribution of these variables across agents corresponds to the penetration of these norms into the population.
● There are three main behavioral regimes implemented, with an additional noise/drift:
(1) − Rational updating (The optimal strategy given willingness to punish in the agent’s neighborhood and the severity and certainty of the central punishment.) This method is designed to represent the viewpoint of classical Economics: the omniscient, unerring and selfish image of economic man. Agents are supposed to have rational expectations on the punishment they face, and set their level of cooperation accordingly. Since the enforcement of cooperation is supposed to be always either costly or beneficial for the agent (regardless of the state of the environment) where a rational updating can be captured simply by the drift, this method for willingness to punish captures instead its sensitivity to the costliness determined by the average defection level in the neighborhood.
(2) − Imitative updating (Copying the strategies of neighbors, with adjustable bias towards the successful.) Imitation as we have seen is a very important phenomenon in social life, most closely coupled with Sociology. There are two typical manifestations: unconditional (adapting to the majority or the typical) and conditional imitation (copying successful examples). In Contributron both are implemented, with a parameter allowing for a smooth adjustment of the degree of payoff-biasedness. Its mechanism is identical for both behavioral dimensions.
(3) − Direct effects (Direct reaction to punishment) Aversion of pain influences the behavior of most living creatures, and humans are no exception. In the first part we have familiarized ourselves with the notions of Psychology building schools on the idea of conditioning. Although in social life disapproval and monetary penalties differ from physical pain, people tend to yield to these kinds of pressures, too,327 as also demonstrated by economic experiments. For willingness to cooperate this regime raises the probability of contribution for the agent directly after being punished, while for willingness to punish this effect depends upon the number of punsihement events seen in the neighborhood, capturing the expressive function of law and the by-stander effect. To allow for differences in the effects of central and peer enforcement both variables have separate parameters controlling sensitivity to the two sources of punsihment.
(4) − Noise / Drift: Both behavioral dimensions include a noise / drift component, a normally distributed random variable independent through time and across agents with adjustable mean and standard deviation. These are added to each agent’s behavioral variables, representing either a natural bias in behavior or some exogenous influence, imperfect replication or transmission, and the mutation of behavior. For willingness to punish the
327 See the examples in Chapter 7 in Part III.
- 80 - mean of the drift can be conditional on the defection level of the agent, reflecting the observation that defectors are usually less willing to enforce.
● As mentioned, there are two sources of punishment: a schematic central authority and the neighboring agents in the network. The effects of the two types can be set independently, partly through the parameters of the updating mechanisms, partly through their severity (the magnitude of the penalty). Agents have a third variable describing their relative success to which endowment and penalties are added in each turn. While certainty for the agents is endogenous (their willingness to punish), the same for the central authority is given by a parameter.
● Heterogeneity is a fundamental characteristic of real-life groups and societies. In the first part we have seen the underlying mechanisms responsible for divergence of personalities, and also mentioned some experimental evidence. For a higher degree of realism, Contributron allows for three kinds of heterogeneity: firstly, different behavioral patterns can be mixed in the same agent, secondly different agent types can be combined in the population and thirdly connections of the social network can be set up arbitrarily. The first two types of heterogeneity can be achieved simply by altering parameters: for behavioral heterogeneity within one agent type we simultaneously set multiple parameters to values other than zero, for population heterogeneity we define different agent types by individualizing parameter settings. (All parameters can be set individually and independently for each agent.)
● There are several built-in parametric network types that can be generated automatically by the executable, with the possibility of defining custom networks. By today there is no doubt any more on the relevance of institutional arrangements concerning socio-economic phenomena. In this tool the experimenter has total control over the structure of the social network hosting the agents.
● There is a wide assortment of exported data from the data generating part that can be loaded into Mathematica for analysis and for producing further statistics. All exports are available both as a population average and at the individual level. Furthermore, all internal events (contributions, the number of checks and punishments) are accessible, greatly widening the range of applications of the model. To speed up simulation, the frequency of data export is adjustable.
● Due to Mathematica’s capability to handle standard text files, all settings including those entered via the ini file can be programmed, which makes it possible to set up complex experiments that can be run for a long time without human intervention.
2.2.2. Formal Description
This section delivers the detailed technical description of the model.
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2.2.2.1. Implementation
The data generating part (Contributron.exe) is written in C++. It receives settings and parameters partly from a text file (Contributron.ini) and the Mathematica interface. The latter controls the executable and it contains special routines written by me for facilitating data handling and analysis in addition to all the standard capabilities of Mathematica. Data is exported from the data generation part into a working directory, from where it is automatically loaded into Mathematica for analysis. The executables are available for PC (Windows), but in principle any system that is able to run Mathematica and a C++ compiler are suitable for Contributron.
2.2.2.2. Agents
In this model each agent has three variables updated in every turn. The changes of these variables constitute the dynamics of the model. Their movement is governed by their past values and the parameters and other settings (including network structure). The variables are:
Boldness (B) – A real number between 0 and 1, the probability of defection (or the proportion of required contribution that is not paid in)328 Watchfulness (W) – A real number between 0 and 1 (or WMIN and WMAX), the probability of checking each neighbor’s actual cooperative behavior329 Reputation (R) – A real number (can be negative), an indicator of the relative success of the agent in society.
When updating limited parameters would bring them outside their band, they are placed back to the border value.
2.2.2.3. Parameters
There are two kinds of parameters. The first group consists of those controlling the technical functionality of data generation and global parameters that concern all agents or general features (for example tax rate.) These parameters are set and handed over directly from Mathematica to the data-generating executable before each run of simulation. The second group of settings is contained in a file called Contributron.ini. These on the one hand include descriptors of the network structure, initial conditions and shuffling. Secondly, all global parameters normally given in Mathematica can be set individually for any agent here. This way, by defining different agent types heterogeneous populations can be assembled. (E.g. separate income groups, etc…) This file must be placed into the working directory of the executable. The location of the actual working directory can also be set in Mathematica.
328 Which can be set by parameter bit. 329 In fact, B and W represent a mixed strategy in game theoretic terms.
- 82 - Below is a description of the parameters controlled directly from Mathematica.330 The experimenter can set them up for running simulations one by one, or specify a rectangular grid of arbitrary dimensions for a succession of runs to be executed automatically.
2.2.2.3.1. Technical Parameters
Seed (SEED): The seed for the random number generator Generations (G): It specifies the number of periods to be simulated. Runs (RUNS): The number of runs to be executed with the same parameters, but different SEEDs. When it is greater than one, the average of all simulated data is exported. Step (STEP): Data is exported in only every STEPth turn. Control Bits (CB): Collections of Boolean parameters in double word (32 bit) parameters, controlling various aspects of the execution.
The most important CBs: Continuous Contribution (CB_CC): If it is 1, the agents contribute (1−B)*TR*E, in every turn, that is contribution is partial and non-probabilistic. The probability of getting caught, however is the same as with discrete defection (CB_CC=0). (It is proportional B). When CB_CC=1, PPE and CPE are multipliers that define what multiple of the amount not paid in in the last turn is the penalty. (E.g. PPE*B*TR*E). When CB_CC=0, B is the probability of shirking: The agent pays 0 with probability B, and full expected contribution, Tr*E, with probability (1-B). Symmetric Network (CB_SN): When set to 1, random network types produce symmetric output that is all connections are symmetric: if an agent monitors someone, he will be also monitored by her. When it is one and a custom network is entered, the upper triangle of the connection matrix is transposed and pasted into the lower triangle, thus it is enough to fill in the upper triangle. Averaged Export (CB_AE): When 1, alll exported data is averaged over the last STEP turns elapsed since the last export. When 0, the data of the actual turn is exported only. Data Export (CB_DE**): Various data exports (** indicates the abbreviations of different data types) can be switched off to speed up simulation when they are not necessary. 1=Data export is on. Watchfulness Update Direct Self (CB_WUDS): If 1, the direct effect is also added to W when the agent himself is punished. (It represents Socialization by Control from Kosfeld and Huck (1998).) Self-Punishment (CB_SP): If 1, the agent monitors and punishes himself like anyone else in his vicinity. (It is the representation of an internalized norm or guilt or cognitive dissonance.) PPE is Penatly (CB_PPEP): If 1, the PPE of an agent is used to determine the sum to be deduced from those punished by the agent, if 0 the sum to be deduced from the agent when he is punished by others.
330 And loaded from the ini file for agents differing from the global type when simulating heterogeneous populations.
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CB_WUDS and CB_SP are possibly individual, that is they can be set independently for all agents. The rest of them are global, affecting the whole system.
2.2.2.3.2. Policy Parameters
Policy parameters represent real life phenomena that in real-life (to some extent) can be influenced by central authorities.
Tax Rate (TR): A number between 0 and 1. It gives the fraction of the endowment of the agent which is expected to be contributed to the group. Central Probability (CPR): A number between 0 and 1. The per turn probability of that the central authority checks an agent. Central Penalty (CPE): In the discrete contribution case this amount (negative in most cases) is added to R whenever the central authority finds an agent shirking. In the continuous case it is a multiplier to get the amount of punishment from the contribution retained: TR*E*B*CPE (All of the above can be individualized.)
2.2.2.3.3. Structural Parameters
These parameters control the structure of the simulated social network.
Population (P): When agents and the network is not given explicitly, this parameter sets the total number of agents Sight Range (SR): Has different meanings in different networks. In ring and linear networks, it gives how many of their neighbors agents see on the array. They see symmetrically, but when SR is odd, they see one more agent on their right (from those with higher index). On linear networks agents close to the edge see less agents accordingly. On a Uniformly Random network everybody has this many neighbors, and on a Probabilistically Random network, this is the mean number of connections. When the connection matrix is given explicitly, SR is ignored.
2.2.2.3.4. Updating Parameters for Reputation
These parameters determine how Reputation changes (except due to the policy parameters.)
Endowment (E): The value added to the R of the agent in each turn.
- 84 - Reputation Attenuation (RA): R is multiplied with this number in every turn. It represents that past events may become gradually less important. (Alternatively, an interest rate, if greater than 1.) Peer Cost (PC): The amount is added to R for each punishment the agent exerts on his peers. It may represent multiple effects. Firstly it can be hypothesized that agents must sacrifice resources to carry out the punishment (which makes their status less desirable), on the other hand the society may endow punishers with esteem to keep free-riding down (which can makes them more of a success.) Observe that PC is not considered directly in the agent’s decision about W, it only describes how his relative status in the society is modified by his punishing. (Nevertheless, through payoff-biased social updating it can be fed back on W, of course.) The agent’s aversion from (or inclination to) punishing is captured by the updating parameters for W including the drift, not PC. Note that in the continuous contribution case (CB_CC=1) PC is not proportional to the amount not paid in like punishment. Peer Penalty (PPE): In the discrete contribution case this value (normally negative) is multiplied by the number of punishments received from peers (including self-punishment) and the product is added to R in every turn.331 In the continuous case the number of punishments is multiplied by TR*E*B*PPE to get the punishment that is it will be proportional to the retained contribution, similarly to central punishment. When PPE is given at the individual level, CB_PPEP determines if it is the sensitivity of the agent to peer punishment (CB_PPEP = 0), or it measures how strictly he can punish. In the first case PPE is deduced from his R when he is punished by another agent, in the second case it is deduced from the agent he punishes.
2.2.2.3.5. Updating Parameters for Boldness and Watchfulness
These parameters describe how Boldness and Watchfulness changes due to rational maximization, peer and central punishments, imitation and a noise component. Watchfulness Minimum / Maximum (WMIN, WMAX): Real numbers between 0 and 1. The experimenter may floor / cap W at any level between 0 and 1. WMAX represents the joint effects of two things: firstly, limited transparency (i.e. detection of defection may be difficult)332 and secondly agents with many connections may have less energy to detect each defection. WMIN captures that there may be some baseline willingness to punish, even without societal or psychological effects.333 The following table summarizes the parameters used to control updating B and W. It contains the most important effects working together in forming human behavior as demonstrated in the first part.
331 As a matter of fact, peer penalty can also be thought of as being exercised by the authority, where only reporting is done by the peers. Besides, observe the factors that the ‘close-knit’-ness of a community depends: SR (or the number of connections set manually), which determines the density of the network and PPE with parameters of social updating and PC, which corresponds to the strength of these links. 332 Remember that it required an extra parameter in Axelrod (1997). 333 As suggested by evolutionary theories and verified by economic experiments.
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Boldness Watchfulness
Economic Rationality BUR WUR
Psychological Direct Effects BUDC, BUDP WUDC, WUDP
Social Imitation BUS, BUSC WUS, WUSC
Drift / Noise BUNM, BUND WUNM0, WUNM1, WUND
Table 4 – Parameters for Boldness and Watchfulness Updating
Boldness Updating by Rationality (BUR): A weight (between 0 and 1) to determine the displacement in B towards the level that maximizes expected income (Bm). The payoff maximizing level is calculated as follows: In the discrete contribution case (CB_CC=0) the agent (with index n) considers the extra expected income from not paying the tax:334
TR** E++∑ Wi PPE CPR * CPE , (2.1) i
335 When it is greater than 0, Bm is 1, and 0 otherwise. In the continuous contribution case (CB_CC=1) the agent finds his payoff maximizing B level by maximizing his expected income (below) with respect to B.
(**)(1(TR E B+++− B∑ Wit, * PPE CPR * CPE ))(1) E TR (2.2) i
The payoff maximizing level is given by:
1 Bm =− (2.3) 2(PPE∑ Wi + CPR * CPE ) i
(Or 0 or 1, should the above expression fall outside this range.) In either case the contribution of rationality to the change in B is calculated as a weighed sum:
BRnt,,=−((1BUR ) B nt , + BUR * B m ) − B nt , = BUR ( B m − B nt , ) (2.4)
334 Mind that PPE and CPE are usually negative. 335 Note that all parameters represented in these formulas can be given individually, thus they may be different for all agents.
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This component represents rational thinking, the traditional view of Economics.
Watchfulness Updating by Rationality (WUR): This effect works less similar for B and W than the rest. The reasons are on the one hand that experimental results indicate the lack of strategic motives in punishment, and on the other hand that punishing is either always costly or beneficial regardless the variables of neighbors or the agent itself, which can simply be captured by the drift. (If it is costly then the optimal level would always be 0, otherwise 1.) This is why WUR is aimed at another closely related phenomenon we discussed earlier: cost sensitivity. When an agent is in a high B environment, the same W level for him would demand more effort, as he would need to exert punishment more often. To reflect this change, WUR modifies the drift in W (the mean of the noise component) depending on the level of 336 average B in the neighborhood of the agent (excluding himself) : WUR*Baverage is added to it. (Which is why WUR is naturally negative.)
BU Direct Central, BU Direct Peer, WU Direct Central, WU Direct Peer (BUDC, BUDP, WUDC, WUDP): The following two numbers are added up to give BP,n,t, the psychological component in moving B. Firstly BUDC, whenever the central authority punishes the agent. The other value is BUDP first multiplied by the number of punishments received from peers. This effect for B represents on the one hand conditioning, where by exposure to aversive experiences the agent learns to avoid certain situations. On the other hand it can be interpreted as learning from own experience that is a cognitive reaction. WUDC and WUDP are the analogues of BUDC and BUDP for Watchfulness. They work, however slightly differently again to correspond real life more closely. WP,n,t is given by adding up the following. WUDC times the agents punished by the central authority in the vicinity of agent n, and WUDP times the number of punishments exerted by the agent’s neighbors. Self punishments are not counted, and those cases when agent n is punished are only counted when CB_WUDS=1, to capture Socialization by Control. WUDC represents the expressive function of law, WUDP the by-stander effect. Nevertheless, depending on assumptions, WUDP also can be interpreted as the behavioral effect of spitefulness (when CB_WUDS=1) or as a channel of norm transmission.337 Direct effects are able to generate a positive feedback,338 typical in norm dynamics.
336 Observe that the expected number of punishments exercised by an agent is proportional to the average B in his neighborhood. (Just like to his own W.) In fact, there is an alternative interpretation for WUR. Welch et al. (2005) found convincing empirical evidence for that high perceived tax evasion in a community (tax is a form of contribution to common objectives) makes people judge this act less harshly; which, in effect, is the same as if their W would be decreased for economic reasons. 337 The difference between the mechanisms of direct effects for B and W requires a bit of explanation. Unlike with B where it is reasonable to assume that being punished has a direct effect on the individual’s shirking behavior, it is less obvious if the same effect directly affects the willingness to punish. On the other hand there are signs that others presence and behavior do have an effect on it (the by-stander effect), and that punishment on the part of the central institution has an effect on the willingness to enforce pro-social behavior of those not punished directly (the expressive function of law). Also recall that being surrounded by a large number of punishers facilitates punishment, and punishment is an overt signal of being a punisher. This way it becomes possible to accommodate additional assumptions: we can assume that punishment strategies can be observed and copied directly (through imitation) or that they only have an effect through observation of the actual behavior. Cascading phenomena like ostracism and lynching also suggest that there is a positive feedback in punishment behavior, which is not attainable purely by imitation. It is also a valid idea that with B, observing others behavior (whether they are shirking or not) could have a direct effect on behavior in a similar manner to W, but the direct-
- 87 - Finally, both BP,n,t and WP,n,t are checked so that adding to B and W they do not exceed their respective bounds.339
BU Social weigh, BU Social Conformity index (BUS, BUSC; WUS, WUSC analogously): BUSC and WUSC are used to determine the curvature of two continuous curves connecting (0,1) and (1,0) on R2. These curves give us weights for weighing strategies by their successfulness separately for B and W. Being an original idea that might be used elsewhere, I would like to describe this one in a bit more detail. To obtain the curve, taking x=BUSC, we draw a pair of Bezier curves340 with control points {(0,1), (0,2x), (x, x)} and {(x, x), (2x,0), (1,0)}, if x<0.5, and {(0,1), (1−2*(1−x),1), (x,x)} and {(x,x), (1,1−2*(1−x)), (1,0)} if x=>0.5. Attaching the two halves, it gives a smooth curve passing through (0,1), (x,x) and (1,0), which is symmetrical to the y=x line and at the same time tangential to both axes. (At least where x<0.5). By moving x from 0 to 1, we can gradually modify the curvature. When x=0, we obtain weights representing payoff-biased transmission (only the strategy of the most successful agent is copied), and x=1 conformist transmission341 (when each neighbor’s strategy is averaged with equal weights). (We have seen in the first part that these are the most important types of transmission. I have also referred to several models examining them.)342 With x=0.5 we have a straight line generating linearly diminishing weights from the most to the least successful agent. All other x’s give a case in-between the above. Weighs are taken from x=0 for the most successful, x=1 for the least successful neighbor, and all others ordered by their relative success (R), placed equidistantly through (0,1). Weights are normalized to add up to 1, of course.
effects mechanism for B as it is implemented appears to be much more important, and we need to be parsimonious to some degree. Just to remark, there is another possibility not included in the model, that of a cross effect: seeing others punishing or being punished could affect B – that is learning from others’ example. In fact, BUR is similar to this and it fits more closely classical postulations in economics, namely that of perfect knowledge. 338 E.g. when an agent punishes another, the punished agent’s W goes up, thus he will punish the first agent more likely, whose W goes up and so on. There are more involved ways, too: for example with a stronger downward drift in W at higher B, it is easily seen that the more people has high B, the more successful this strategy can get. 339 Observe that the direct effect differs from the other two because here we do not have an implicit target value with which the original value of B and W could be weighed. In fact, there is an implicit target value that can be set by the experimenter, and the weight is the relative number of punishments the agent sees (relative to the total number of punishments possibly visible for the agent). This target value is the original value of B plus the possible number of punishments in the neighborhood times the respective parameters (BUDC, BUDP, WUDC, WUDP). 340 There are many sources on the Internet for Bezier curves. For example one good introduction can be found at http://www.ibiblio.org/e-notes/Splines. 341 Welch et al. (2005) also supports that people in a community featuring high tax avoidance will themselves be more inclined to cheat on tax subsequently. 342 See on page - 57 -.
- 88 - 1 1
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Figure 1 – Weighing with Bezier curves: Bezier curves with curvature parameter (BUSC or WUSC) from 0 to 1 by 0.1 steps (left); weights obtained with curvature parameter 0.3 (right).
After computing this weighed average of strategies (Bsoc and Wsoc) – in which the strategy of agent n is also included −, the social updating factor is given by
BSnt,,=−(1BUS ) B nt , + BUS * B soc − B nt , = BUS ( B soc − B nt , ) , (2.5)
And its analogue for WS,n,t.
BU Noise Mean, BU Noise Deviance, WU Noise Mean 0, WU Noise Mean 1, WU Noise Deviance (BUNM, BUND, WUNM0, WUNM1, WUND): Finally two independent normally distributed random variables (noise components BN,n,t and WN,n,t) are calculated. These capture on the one hand a drift that may result from a natural psychological inclination for shirking (or contributing or punishing343) either because of the genetic heritage or some kind of external temptation, or the tendency of social norms that without incentives, practice and reinforcement, they may slide into oblivion. 344 The speed of this drift can be set by modifying the mean of the noise parameters (BUNM, WUNM0 and WUNM1). Watchfulness has two parameters for this, so that it can be made dependent on the level of B of the agent, because it is reasonable to assume that with a high propensity to defect, one is less inclined to obey an enforcement norm of cooperation. This is why the experimenter may set WUNM0 (the speed of drift per turn in W when B=0) and WUNM1 (this speed when B=1) independently, and speeds for all other levels of B are acquired by a linear interpolation of these two values.345
343 We have seen how biological evolution cross-linked with social evolution might have produced genetic embedment of certain social behavior. For example, group selection gives an explanation why a tendency for punishing can be supported genetically, while individual level selection can account for the leaning for free- riding. 344 Like conditioned behavior. (Atkinson (1992) p.237.) 345 An apt quotation from Kahan (1997): a “belief that criminality is rampant alters individual’s evaluation of criminality.”
- 89 -
Mean of WUNM0 Noise (Drift) in W
B=0 B=1
WUNM1
Figure 2 – Mean of WN as a function of B set by WUNM0 and WUNM1
Recall that WUR also modifies the mean of the noise. That, however, makes it dependent on the average B in the neighborhood of the agent. Notice that this defines the drift as a linear function of two variables: the agent’s own B and the average B of his contacts. With the three parameters involved (WUR, WUNM0, WUNM1) we can move the plane of the function arbitrarily. On the other hand, imperfect perception and replication 346 , plus trial and error learning 347 (experimentation with strategies) are represented by the standard deviation of these random variables (set by BUND and WUND). At the same time, this noise is the source of the raw material of evolution: variability.
Having calculated the effects of rational calculation (BR, WR), the direct psychological effects of punishment (BP, WP), the effects of social imitation (BS, WS) and the noise components (BN, WN), we add up these to the present value of B and W of each agent, and apply the (0,1) bounds for B and (Max(WMIN,0), Min(WMAX,1)) for W, to get the B and W for the next period. The above specification shows that central and peer punishment can influence the strategy of agents in a variety of ways. It should also be noted that the effects of central (formal) and peer (informal) punishments can be set independently both for the psychological effect and concerning reputation.348 The following figure summarizes these channels with the most closely related parameters and variables.
346 Which can result from psychological imperfection or external perturbations. 347 Whose significance was stressed earlier. 348 Refer back for example to Salem and Bowers (1970) who found that severe formal sanctions in the first place cultivate the normative climate of the community, and usually the latter is what is more directly effective in suppressing deviance. (For such a situation we should have a relatively high WUDC and a high BUDP and PPE.) They also show, however, that this connection between central sanctions and peer pressure varies concerning different offences. Also recall the different ability of formal and informal punishments in dealing with instrumental and expressive actions. Besides, Kahan (1997) mentions that defying central authorities can confer a badge of honor to the agent, which implies a totally contradicting influence of central and peer punishment on
- 90 -
Central Punishment Peer Punishment
Deterrence CPE, CPR PPE, W
Direct Effect BUDC, CPR BUDP, W
Imitation BUS, BUSC BUS, BUSC
Inducing Watchfulness WUDC WUDP
Figure 3 – Channels for punishments to influence Boldness with related parameters and variables An important thing to remember is that ALL parameters are ADDED to all sums, implying that costs and penalties should be normally negative.
2.2.2.4. Exports
The following data is exported from the data generation part:
● Boldness ● Watchfulness ● Reputation ● Contributions ● Central Checks ● Peer Checks ● Central Punishment Received ● Peer Punishment Received ● Peer Punishment Inflicted
All exports are available for individual agents and cross section averaged over all agents. (It is much quicker to do it in C than Mathematica). Any of them can be switched off by the corresponding control bits to speed up simulation when they are out of interest. Moreover, parameter STEP controls the number of turns between data exports, and CB_AE sets if these exports are averaged over all the turns in between.
2.2.2.5. Network Types
Reputation. (This situation also can be captured by the model by setting CPE and PPE to values with different signs.). But even if things are not so bad, this suggests that, the expressive function of law can affect people differently than they each other. Another important argument for separate parameters for central punishment is that its severity is a policy question unlike in the case of peer punishment. Furthermore, the number of possible peer punishments in an agent’s neighborhood grows much faster with the number of connections than the number of potential central punishment events, and this effect can only be controlled if we have distinct parameters for the two.
- 91 - The following network types are available for generation:
● Custom (the network matrix set explicitly) ● Custom Randomize (Having loaded a Custom matrix, SR pairs of its elements are swapped with each other. If we are using a symmetric matrix (CB_SN=1), the mirror positions are also exchanged. Useful to control the level of connectedness with (semi-)isolated sub-networks without affecting the overall connectedness.) ● RING (An array with periodical boundary conditions, all agents are connected to SR neighbors symmetrically) ● LINE (A linear array, agents are connected to SR neighbors symmetrically, but those near the edges are connected to less) ● Random Constant Regular (RCOR, A constant network, all agents are connected to SR neighbors, connections placed randomly) ● Random Constant Probabilistic (RCOP, Similar the RCOU, but SR is the average number of connections, all edges created independently with identical probability.) ● Random Changing Regular (RCHR, Similar to RCOU, but network connections are recreated in each turn) ● Random Changing Probabilistic (RDHP, Similar to RCoP, but network connections are recreated in each turn) ● FULL (All agents are connected to each other.)
The network matrix and the directives for network generation should be entered in contributron.ini. All special network types (except for FULL) use individual SRs when possible. A Mathematica function, blockNetwork[] makes it possible to generate isolated sub- networks within a super-network which in turn can be loaded as a Custom network. The sub- networks can be connected inwards with any of the pre-defined network structures. It can be used to simulate real-world experimental setups.
2.2.2.6. Initial Conditions
Initial conditions can be entered through contributron.ini. They can be set independently for all agents or types, either supplying concrete values or a range within which the program generates random values with a uniform distribution.
2.2.2.7. Agent Shuffling
Agents can be created by type: the experimenter can describe different agent types, and give a number of instances to be created. By default agents are created in blocks, however, this can be randomized by a shuffling procedure349. This, of course, has a point only when the network is not random. There are three types of shuffling implemented:
349 Usage of random initial conditions and shuffling are both usual in the literature.
- 92 - ● Randomization – Agents are put in a random order (each agent has an equal probability to each place.) ● Re-randomization − Agents are reshuffled by the previous method in each turn to achieve the “Strangers treatment”, a popular experimental method. Most useful with isolated sub-networks. ● Swapping – The original order is randomized by swapping two randomly chosen agents at a time. The number of such swaps can be set by the experimenter.
2.2.2.8. Initialization
Before the model could be run, it needs to initialize, create the agents and set up the network. It is done in the following order.
1.) Receiving parameters from Mathematica. Loading additional data from Contributron.ini 2.) Generating / loading agents (including initial conditions) 3.) Shuffling agents 4.) Generating / loading network 5.) Simulation
The distinction between generation and loading is based on whether agents and the network are explicitly given by the experimenter. If so, they are loaded, if only agent types and their quantities are given, or a network type is described, they are generated. Shuffling agents is only executed on request.
2.2.2.9. Simulation
After the initialization, the simulation commences. The timing of one turn is as follows:
1.) Endowment arrives 2.) Contributions are made 3.) Punishments are executed 4.) Data export 5.) Updating Watchfulness 6.) Updating Boldness
There are three notable points in this list. First, data is exported before updating, because updating only has an effect in the next turn, and the experimenter is probably more interested in what caused the outcome of the turn than what is the effect of the outcome on the variables. The second point is that Watchfulness is updated before Boldness. It must be so, as Boldness contains a rationality component which is calculated basing on rational expectations that is supposing that agents know the true risk in defecting in each turn. Finally, data is not exported in every turn.
- 93 - In Appendix 2 the reader may find a detailed flowchart visualizing the structure of the data-generating part.
2.3. Discussion
In this chapter I would like to add a few comments to the model just described and call back briefly a couple of ideas from the first part putting them together with the elements of my model. First of all, the reasons behind the design of network handling in my tool. We have seen that societal institutions have a major impact on social outcomes. On the one hand, it has been mentioned that several theoretical studies from game theory to simulations pointed out the sensitivity of results to the structural setup of the network involved. On the other hand, social institutions as instruments of enforcement also have been demonstrated empirically to be able to complement legal systems and markets in fostering pro-social behavior. The Contributron fully acknowledges the first, and also makes important experiments possible for the second issue, while keeping the road open for further development. Furthermore, we have seen the difference between the way analytical methods and simulations treat social connections: analytical models mostly use mean-field analysis and random pairing of agents while agent based models are able to handle various regular and irregular preset networks. My model creates an opportunity to compare the two in a quick and standardized way. Second, agents. What should always be kept in mind is that this is a behavioral model. In other words, what is modeled is not mental procedures, like maximization in standard Economics, but action directly. What induces a certain action is another question. In what has been said I tried to build up a picture of man: a faulty, socially influenceable and psychologically conditionable being, who at the same time has rational thoughts as well. This image suggests for example that there is an instinct, an automatism behind the direct effect in B when the agent is punished. Nevertheless, one might also reasonably stand for that this is a rational act, learning by experience, and cooperation is raised by having more information about the high level of expected punishment in the forthcoming turns. Likewise, in addition to the social and psychological explanations given above, there are many conceivable factors affecting punishment behavior not represented explicitly in the model. For example, recall that punishment is shown to be sensitive for the price of punishment (that is the price of delivering one punishment, not the price change coming from the growth of average B level of the neighborhood handled by WUR), or there can be a metanorm 350 working in the background when people punish or it can be the case that seeing others punishing alleviates one’s internal inhibitions. Once again, in this model behavior and not motivations are modeled and it is the responsibility of the experimenter to consider all factors outside the model that may have an effect on action and to set the parameters accordingly. (For example if he pictures a costlier punishment, he can set say a heavier downward drift, or a weak direct effect. Third, contribution and reputation. First I have to stress that contribution in the model is not necessarily a representation of some material payment. It can be any resource that people are recurringly endowed: time, workforce, attention, etc…, everything that in certain social settings can be sacrificed for the community. It of course implies that having this resource is also good individually, which is also clear form the way the rationality effect is computed. Accordingly, the nature of punishments also depends. Typically, central
350 In fact, a form of metanorms is already in the model: a positive PC with payoff-biased transmission for W.
- 94 - institutions can inflict formal, while peers some kind of informal punishment. As far as the model goes, all that matters is that punishment parameters reflect how these deductions affect the relative successfulness of the agent. All settings: endowment, tax rate, the control bit for continuous contributions, costs and punishments should be made to fit best to the characteristics of the situation in mind. Certainly, different settings result in different output for different situations, so altering settings makes a fast comparison possible between different setups. How the community benefits from the payments is exogenous, the only restriction is that it should not alter the relative ranking of success of the individual agents, which is quite reasonable considering that it is a public good.351 I have already mentioned that Reputation is used in a different meaning than in game theoretic appliances. In my model it shows the relative successfulness of the agent in society352. This is why its global level is indifferent, it can even be negative. (This approach is also present in the literature.353) What also should be seen is that this is a unified measure of success: monetary and non-monetary factors combined.354 As a matter of fact, there would be a possibility to keep two separate variables for them, and determine success by a weighed average. Nevertheless, it would have less additional advantages for the model than it may seem at the first sight. Since punishment, endowment and cost parameters are freely variable (for each agent separately), we can do the weighing on these values, which can generate the same effect on dynamics as the other alternative.355 (In fact, it could make a difference but only if different agents could react differently to the different measures, which is a possible way of extension.) One could argue another disadvantage that the experimenter has no sufficient knowledge about the components status consists of, which, however, is incorrect as everything can be easily reconstructed from the exported data. The setup of the model is similar to standard PG experiments. Here, however, the public good is not paid back to the agents. In fact, it would make no difference, as a payment of equal shares would not alter the relative ranking of the agents, therefore their choices would be exactly the same as this way. Additionally, at least with certain parameter settings (equal E and TR for all), the model can be seen as a Common Pool Resource game, because payment in these cases is tantamount to not withdrawing from the pool. A similar argumentation can be applied for rewarding: we can imagine that those not punished in the model are rewarded more than defectors, which would lead to the same relative ranking and thus to the same dynamics. There is a control bit, which deserves special attention. It is CB_CC by which the experimenter can choose if contribution in the modeled situation is continuous or discrete. The continuous case more suits situations where agents can make a partial contribution (like e.g. payment of taxes or some fee, or the conduct of experimental PG games), while the discrete case covers conditions where it is not possible (like attending meetings or taking part in activities). That obeying a norm is a matter of degree for the discrete case implies that you are more or less willing to act as prescribed (contribute or punish in this case). In real life in addition to the degree of norm adherence, your final behavior depends also on other
351 Nevertheless, if the experimenter thinks otherwise, he can alter the endowment and tax rate of the agents individually. 352 See e.g. Maher (1998) who touches upon relative esteem and its connection to norm emergence. 353 E.g. in Friedman and Singh (2000) 354 Elster (1989) remarks that costliness of punishment is supported simply by its opportunity cost. Observe that this also gives a reason why the cost of punishment can be combined with a material measure of success. 355 Besides, evoke the finding that people do not discriminate between the behaviors of an idol when imitating them (page - 57 -). For the present model it means that B and W are likely to be copied by the same success criterion (R).
- 95 - circumstances, too, partly internal (the risk of being caught, how other people behave), partly external to the model (like weather, mood, etc…). These external effects − by definition − are not part of my model, which uses this probabilistic solution instead to account for them: basically the internal effects adjust the sensitivity to external ones, appearing in the variance of contributions and punishments.356 To get a better insight into this issue, first consider that contributions averaged over a number of periods are asymptotically the same in the two cases (continuous and discrete). What makes the difference here is that the punishment is also made proportional to the defection in the continuous case for which the expected punishment is quadratic in B, unlike the linearity in the discrete case. Secondly mind that if the experimenter assumes either fixedly probabilistic or non-probabilistic contribution or punishment, on the one hand both of them can be set fixed at any desired value, including 0 and 1, separately for each agent, on the other hand weights can be set so high (also higher than 1) that B and W jump between 0 and 1 in effect. Fixing B and W can also be useful if we want to make experiments supposing that there are different types of players (suggested by many economic experiments)357 with little interaction between their behavior (either because they are immune to social influence or because circumstances are such that they are in this sense separated from each other). Be aware, however, that even if we take behavior to be fixed on the short term, it is surely dynamic on the long run: firstly because of the change in the population proportions of different types, secondly because of biological selection that alters types themselves. Fourth, behavior variables. The other two variables Boldness and Watchfulness, measure the probability to defect and punish respectively for each agent that is they describe the behavior of the agents358. These are the most abstract general features appearing in many real-life realizations of the contribution phenomenon. Wherever there is a possibility for free- riding on cooperators, defectors hurt the group as a whole and there is a need for enforcement of pro-social behavior. And enforcement, as we have seen, is often supplied privately and voluntarily. From the picture I have painted throughout the first part these variables are also readily interpreted as measures of adherence to two social norms. The first norm (the Contribution Norm) requires that agents contribute a certain fraction of their endowment (set by TR) to an (unspecified) common goal (public good). The second norm (the Enforcement Norm 359) obliges to punish the defectors among the neighbors of the agent. The crucial difference between the two is that while for the first there is a direct material incentive to breach therefore it probably needs to be externally enforced, the second can become more easily an internalized norm.360 We have seen that social norms are dynamic entities both at the individual and social levels and their existence is a matter of degree. Both dynamics are represented by the set of Bs and Ws: personal adherence is marked by individual variables, while population penetration, say, by their cross section average. However, similarly to what I have said a couple of paragraphs before, one is not obliged to understand these variables as
356 It is notable that this sensitivity is greatest when probability of obeying the norm is 0.5. 357 Reflecting on one of my previous remarks: if we see subjects behaving steadily in experiments (with respect to their punishment activity) it can well result from the utter controlledness of circumstances. Basically, the only element of the environment that is allowed to change is the behavior of the group, more exactly the information about it that experimenters allow to reach the agents. In other words not only social connections are filtered but there are no other external circumstances, either, in the sense just referred above. Therefore behavior may appear much more stable than in real life. 358 Some would call them strategic or choice variables. Because, however, B and W are compounds of various effects from conscious to purely instinctive depending on the assumptions on the mentality behind behavior, these terms does not fit very well to their function. 359 We considered examples for both kinds. See page - 50 -. 360 Evoke what I have said about the internalizedness of primary norms and their enforcement norms (page - 50 - ). This is also the reason why my agents are capable of self-punishment.
- 96 - having anything to do with social norms. Especially when social effects are switched off, they can be interpreted as totally individual features of the agents without any problem. Another issue I would like to draw attention to is the relation between the two dimensions of agent behavior. 361 Although B and W of an agent are not bound together solidly, there are a number of mechanisms through which they influence each other. First of all agents can punish themselves, representing internalized norms and guilt.362 This can drive B down when W is high. Secondly, an agent with a high W punishes defectors in his neighborhood, which through the direct effect of W can increase W in other agents, who in turn punish the first agent and bring his B down, likewise. (This is also one of the appearances of positive feedback in the model, which can lead to an escalation of W.) Similarly, conformist transmission can also channel back the W growth caused by the direct effect first to the W of the first agent, which through self-punishment may push his B down. Thirdly, when the analogue of ‘Socialization through Control’ is on (CB_WUDS=1), high B will generate higher W by the direct effect in W. Fourthly, the noise mean in W can depend upon the B level, which can prevent agents to evolve into states with simultaneously high W and B. Which of these effects govern B and W, of course, depends on the actual parameter settings. Examining the characteristics of norm dynamics, we have found that change of norms exhibit a high level of inertia, which stems in different phenomena from personal habits and internalization to network effects and even genetics. There are several studied on the one hand supplying experimental support363 for it, and on the other theorizing364 based on it. I need to highlight that the updating procedure of both B and W were devised to allow for inertia to
361 Economic experiments show that the two dimensions are connected, however, the link between the two is not always significant (E.g. Carpenter et al. (2004)). Carpenter and Matthews (2004) found “no significant correlation between the amount of punishment one receives [which depends seriously on his propensity to defect] and how much one spends to punish others”. Studies that tried to give an estimation on the population fractions of defectors and punishers indicated that all four combinations exist (defect + not punish, cooperate + not punish, etc… e.g. in Carpenter (2004b) and Falk et al. (2001)). From these, probably the most unusual behavior is when somebody defects and punishes at the same time. They are the so-called hypocrites, who deserve a closer look. These agents are not very numerous, but their presence is obvious. There are at least two possible clusters of explanation for this kind of behavior: firstly selfish reasons: e.g. signaling, securing credibility and others’ compliance to generate future income for themselves, or conforming to a punishment norm (think of for example the protagonist of 1984), and secondly spitefulness. (Altruism is of course out of question here.) While my model can be interpreted to involve spitefulness (by the direct effect on W), strategic punishment is outside its scope. Recall, though, the insignificance of such drives justified by economic experiments. I must remark that in some experiments there is also a small minority (around 5-10%) appearing who defect and punish cooperators (again, most probably by spitefulness). This kind of behavior is not represented in the present form of my model, either, because agents can only punish defectors. This might be reasoned for by asserting that in many real life situations it is impossible or at least much more difficult than in experiments to act that way, for example because punishment is undertaken by reporting to an authority. However, this, together with strategic punishment remain possible directions for future extension. Recall also that long-term evolutionary models (either with group selection e.g. Boyd et al. (2003) or individual selection e.g. in Carpenter and Matthews (2004)) usually work with agents with a fixed mix of cooperative and punitive inclination, whose percentage in the population is jointly governed by success. Nevertheless, as already mentioned, my model is aimed at short term evolution where punishment seems to be governed much less by success (and where behavior and norm adherence is variable not only at the population but the individual level, too). An example where short term evolution is in focus can be found in Kosfeld and Huck (2004) who treat cooperation and punishing behavior separated. 362 A related study is Bowers (1968), who found that a disapproving normative climate affects individuals in two distinct ways: firstly, through the person’s own feeling of condemnation (like guilt in my model), and secondly by normative feelings of others. 363 E.g. in Decker et al. (2003), Carpenter (2004b), Carpenter and Matthews (2004) especially for contributions (short term inertia). 364 E.g. Carpenter (2004a), Kreps (1990) Ch 19. Bowles (2003) in Ch. 2. refers to short term inertia as the rate by which individuals give up one behavior in favor of another, an analogue of (biological) differential fitness.
- 97 - appear in dynamics: their current value (almost) always depends upon their value in the last period as all effects: rational, social, psychological and the noise are added up to it when calculating how they change. How heavy inertia is, though, depends on the parameters controlling the weight of different effects. In the extreme, inertia can completely be eliminated. A few extra remarks on Watchfulness. First of all, probability in W is also used to model limited transparency (that shirking is not always detectable). One can alter this by setting a sufficiently low WMAX, and dividing punishment weights with an appropriate factor. Next, as we have seen, although that people are willing to engage in personally costly punishment activity is widely accepted365, there is not too much experimental evidence on the variability of this punishment behavior. Considering this, one could reasonably build a model with only a static punishment behavior included. Nevertheless, there is no evidence supporting that it is fixed, either.366 On the other hand, taking into account the power of social norms and psychological pressure for conformity, plus what has been said about the interdependence of norm-systems, we just as reasonably can assume that they react to the standard effects like so many kinds of behavior do. In addition, we have also seen empirical examples (like ostracism and lynching) for that punitive behavior is socially embedded as well as scholars advocating it and building models that acknowledge the existence of this phenomenon367. These are the reasons for me to create the possibility for the experimenter to use a dynamic punishment scheme. (Nonetheless, W can be held completely fixed if required.) The effects influencing W are mostly parallel to those changing B. I have already reasoned for why the rationality parameter works differently and what direct effects stand for, but I would like to add a note here on social (imitative) transmission. Its mechanism is the same as that for B, one parameter sets its weight, another the grade between payoff-biased and conformist transmission. Why did I still leave an opportunity for making it payoff-biased, when experiments suggest that strategic motives are less important for punishment? The main reason is that the debate on motives behind punishment is not completely settled yet. As we have seen in many (mainly) long-term evolutionary models and also in those built on metanorms, propensity to punish is directly and exclusively governed by selfish motives and success. I presume that it might not hurt too much to let my model be able to match up with such assumptions as well.368 Fifth, an important note on social updating. To copy the strategy of another agent or a group, our agent should first know about them somehow. I have mentioned that several models use this kind of updating, but the mechanism of how agents can learn about each other’s strategies is not everywhere sufficiently reasoned for. One possible mechanism is this: agents observing each other’s behavior can have an estimate about a probabilistic strategy just by dividing the number of cases they have seen the behavior with the total number of cases
365 Its consequnece for modeling is summarized by Carpenter (2004b), remarking that “positing a preference to punish free-riders appears to be a reasonable addition to standard selfish preferences”. 366 Remember how experiments tend to control against uncontrolled information transmission and informal social influence. 367 Recall the idea of enforcement norms. Besides, e.g. Kahan (1997) directly supports social dependence of willingness to punish by saying “a person surrounded by persons who are morally opposed to crime will be likely to share their aversion.” There are also the two papers by Kosfeld and Huck (1998 and 2004): in the first becoming a punisher is more probable when somebody is punished, while in the second seeing punishers plays a similar role. Moreover, they characterize reporting defection (in effect peer punishment) as a “norm-driven act”. In addition see Friedman and Singh (2000) for a meme prescribing vengeful behavior and offering individuals with an adaptable level of vengeance. 368 Not to mention that symmetry is always nice.
- 98 - when it could possibly be seen (even when detection is limited). In my model agents are supposed to base their social updating on rational expectations partly for simplicity, partly because of the above argumentation, partly because a noise can be added, anyway. Nevertheless it is another direction of extension: the target value of social update could be determined in other ways. Sixth, I need to discuss briefly the representation of the central institution of enforcement in my model. It is admittedly the least elaborate part, basically restricted to a constant probability of monitoring and constant magnitude of punishment.369 It is so, because the primary focus of my research and model has been human motivations and social networks, where centralized institutions of enforcement appear only in special (but important) cases. Nevertheless, examining the interdependence of norm systems and realizing its relevance, I felt compelled to include it at some level at least to signal a direction of further development. However, the two main factors, certainty and severity, are already included, (what is more they can be different for all agents) which makes interesting experiments possible even with the present form of the model. Also note that most formal models up to date did not go further than looking for an optimal but fixed level of detection as discussed earlier,370 for which my model is clearly capable of. Moreover, it can do it with various assumptions about the underlying social structure and the agents. Seventh, output, which makes a wide range of calculations possible. For example we have the number of central and peer punishments undertaken. If we hypothesize a (different) cost for both, we have the total social cost of enforcement. Parameter settings can move it up and down through various mechanisms: for instance CPR on the one hand makes central enforcement more expensive because there are more central checks, but at the same time makes private enforcement less costly because lower defection levels. Nevertheless, it can also induce more private enforcement by the direct effect on W, which further complicates the outcome. In addition it can be assumed that there is some extra return on the public good relatively to private wealth, and so on. One can map the topology of parameter space and look for various optima. The Mathematica interface gives tools to facilitate this process by automatically calculating various statistics from the output along grids of any dimension, it has built-in numerical optimum seeking procedures, and it makes analysis intuitive with graphical output. Not only end-results but various time-series and panel data can be produced as well. This way, both comparative statics and dynamical analysis are readily supported. Although there are many useful Mathematica routines written by me, the experimenter is free to modify, upgrade or customize them to his taste or write his own tools making use of Mathematica’s versatility and flexibility. Last but not least, thanks to Mathematica’s (and C++’s) popularity and the generality of the problem there is a wide community, potentially interested in this new development. Finally, I would like to reiterate the flexibility of the model. The wide parametrization makes it possible to tailor the simulated process as close to various forms of the contribution- enforcement phenomena as most formal models went so far simply by setting a few values. The experimenter is free to choose what effect and features to include or exclude in the dynamics by setting or zeroing out the corresponding parameters. This way my model can be ripped down to the level of analytical models, and the output can be compared with earlier results. Then the experimenter can gradually relax the restrictions and see the consequences of assumptions. Furthermore, several parameters allows for simulation of diverse exotic
369 It is basically a special agent, connected to everybody without B, with a fixed W, and a special value for punishment. 370 On page - 22 -.
- 99 - situations. For example contradicting central and local incentives, anti-conformism, clustered societies, perverse reactions to punishment, etc…371 The number of possible combinations is (almost)372 infinite.
371 It is worthwhile to consider what real life situations correspond to the opposite of natural signs of different parameters. Think of for example the ‘badge of honor’ situation referred earlier. 372 But only because computers are only capable of finite arithmetic. ☺
- 100 - 3.Part III
Results
- 101 - When designing how to organize this part the primary factor that I had to keep my eye on was that Contributron is an experimental tool rather than a usual model. This consideration implies that it makes much more things possible than what can fit into a few dozen pages, and also that it might be used in the future by others, possibly extended or modified to better fit special needs. Accordingly, I had to set special objectives to achieve in this part, the most important of which are:
● The verification and validation of the model. ● The demonstration of - Usage - Experimentation with and calibration of the model - Typical phenomena coupled with different model elements - Different purposes. The presentation of the typical questions that the model is able to address and the typical answers the experimeter can expect ● The basic exploration of the model ● The production of intuition, insights and results concerning salient socio- economic questions
Considering the above requirements I have found the following structure the best to meet them. In chapter 1 I am going to discuss some technical questions for better contextualizing, understanding and using the model. The following six chapters will present results obtained by running the model. The first three of them deals with the three main updating mechanisms incorporated in Contributron. First, (chapter 2) we will examine the rational component, then (chapter 3) we turn to the imitative transmission, and following this to the direct effects (chapter 4). In addition to demonstrating the basic patterns appearing by applying the respective updating mechanisms on their own, each of these chapters concentrates on one or more of the more involved phenomena coupled with them. Whenever necessary, I will also give the reader technical details for setting the control parameters and interpreting the results correctly. The latter three chapters follow a different path, focusing at the most typical uses and special features of the model. The first of them (chapter 5) demonstrates exploring heterogeneous populations and different network effects, two of the main strengths of Contributron. The next (chapter 6) illustrates how to combine output into statistics to measure the efficiency of different central policies or simply different arrangements in terms of total contribution, deadweight loss or a social welfare function. In the final chapter (chapter 7) we are going to see a detailed example on how the model can be calibrated to experimental data, how it can be used to augment our understanding of empirical findings, and formulate new, testable hypotheses. (Observe the span from technical and theoretic questions towards more practical and empirical ones.)
3.1. Analytical Findings
This chapter discusses three selected topics: the first proposing an idea to connect utility-based maximization with inertial weighing of behavior, the second casting light on some important consequences of network structure and the third delivers details on compensating for population changes which is needed for the correct usage of the model.
- 102 - 3.1.1. Behavioral Weighing and Utility-Based Maximization
Weighing plays a crucial role in updating B and W. Some of the parameters (BUR, BUS, WUS) are used directly as weighs, while others (BUDC, BUDP, WUR, WUDC, WUDP) can be interpreted as setting an implicit target value to which the weighs are endogenously given by the actual values of the variables of the model. A note is appropriate here to signal the connection between the behavioral updating method of weighing and the cognitive notion of maximization. Consider the following weighed sum determining the value of some variable to be updated for the next period:
xtt+1 = α xxˆ +−(1α ) (3.1)
In other words the value of the variable in the next period is obtained by weighing the value of the variable in the current period and an (externally given) target value. (In our case α can be for example BUR, xt the Boldness of some agent in period t, and xˆ is Bm that is the target value, where the expected income is maximal.) Now consider the following utility function:
22 ux()(1)(tttt++11=−αα x − x ) − ( x + 1 − xˆ ) (3.2)
The intuition behind it is that the agent values negatively both the displacement from the original value xt (which essentially results in inertia) and the distance from the target value, but with different weights, summing to one. If we maximize this with respect to xt+1, we get exactly equation (3.1) as the optimal value. That is there is a direct link between the behavioral rule of weighing and the cognitive model of maximization. This result is not restricted to one target value only. We could add further ones to equation (3.1) with their own weights and modify the utility function accordingly to get back the weighed sum as the optimal value, similarly to the way Contributron uses multiple weighed values for updating. Furthermore, if agents have a multi-dimensional strategy space, x, the target value and α should be vectors, simultaneously determining the complete strategy of the agent for the next period.
3.1.2. Connectivity of Networks
Contributron has a number of simple built-in network types that can be generated automatically using a few parameters. It will be useful later on for understanding certain phenomena of model output to examine one of the most important features of these networks: some aspects of their connectivity. More closely, what we are going to see here is a special aspect of it, that can help us to capture why agents arranged one way converge faster or better to equilibrium values than others, namely the average distance between two randomly chosen agents. There will be many examples with imitative agents, when information about the optimal strategy from agents already close to it can only spread following network routes, so it is instructive to know how the distance between the imitating and the imitated works out on
- 103 - different networks. (Of course, networks and distances are important not only for imitation, but also for other updating mechanisms, in the first place for the spreading of W levels by WUDP, which in turn can affect B, too, in various ways.) Let us consider first random networks. Then the probability of that there is an immediate link between two arbitrarily chosen agents is q=SR/(P−1). This is directly given for probabilistic networks, and it is also not too hard to see for regular ones.373 Moreover, this is true for both symmetric and asymmetric networks. (In the latter case it is the probability of a one way link.) Then, the probability of that a link of length k exists between two randomly chosen agents is given by:
⎛⎞P−2 ⎜⎟ Pe(,) k q=− 1 (1 − qk )⎝⎠k −1 (3.3)
where P is the Population. The probability of that the shortest link is of length k is:
⎛⎞k −1 Ps(,) k q=−⎜⎟∏ (1 Pe (,))* j q Pe (,) k q (3.4) ⎝⎠j=1
While the probability of that the two agents are isolated (there is no route of any length between them):
P−1 Pnc() q=− 1∑ Ps (,) k q (3.5) k=1
And the expected distance between them, supposing that a link of any length exists is:
P−1 Era() q= ∑ Ps '(,)* k q k (3.6) k=1
Where we have renormalized Ps(k,q) so that the probabilities sum to one the following way:
Ps(,) k q Ps'( k , q ) = (3.7) (1− Pnc ( q ))
Turning to the LINE network, first we realize that here agents are always connected. Next, considering that two randomly chosen agents can be anywhere on the line and using a geometric method instead of integration to calculate probabilities, while not forgetting that
373 In the case of symmetric networks q is the probability of a two way link, while for asymmetric networks a one way link. Accordingly, when we are talking about a route or a link below, when we refer to asymmetric networks, it should be understood as a one way route.
- 104 - depending on P and SR some jumps might be shorter than SR, the expected distance between two randomly chosen agents is the following:
Eli(()) j q= j *(2−+ j ) r−1 ∑((kkj+ 1)*(0.5−+ )*22 )) (3.8) k=1 (1−+rj * )2 * ( r 1)
Where j=SR/2/(P−1) (=q/2) and r=[1/j] (That is the integer part of 1/j). The same for the RING network is
r Eri(( j P , SR ))=++−∑ k * j ( r 1)*(1 r *) j (3.9) k=1
Where j=SR/P. (Observe that this expression depends on SR/P instead of q=SR/(P−1) like the former ones. This discrepancy, however, diminishes as P gets large.) If we plot Era(·), Eli(·) and Era(·) (the lines indicated below as Line, Ring and Random) and Pnc(·) (as P(NoCon)) as functions of q (P=33, SR={1,…,32}) we get the following picture:
Min . Steps 10
8 Line
6 Ring
4 Random
2 P NoCon
SR P−1 1 1 3 H L 1 4 2 4 êH L Figure 4 – Expected distance (minimal number of steps needed to reach one agent from the other) between connected agents on various networks and the probability that two agents chosen at random are isolated on a random network.
Not surprisingly in all networks the average distance rises as we approach 0 with q. The reason why random networks turn around is that calculating distance we only consider those agents who are not completely isolated from each other. (We can see that the probability that two agents are isolated rises from around q=1/8 suddenly.) Theory supports intuition in that LINE is the worst connected network. Observe also that even if we have q=1, the average
- 105 - distance is still higher than 1 for it. Remember that agents on both LINE and RING see equal (or only one more to one side if SR is odd) agents on both sides, which is simply truncated in the case of LINE, allowing for agents on the extremes not to be directly connected even when SR=P−1. Also note that the other two network types both converge to one. RING is better connected than LINE, because in this case we have two alternative directions to start from one agent, from which we can choose the shorter. What is even more important, though, is that the random network is the best connected one in this respect. It is due to what I am going to refer as ‘small-world’ links, shortcuts that make it possible that information be transmitted and spread faster, without having to get through long distances around the RING or along the LINE. As we can check, this is true even where the probability that two agents are separated is low thus not influencing the expected value too much. On the other hand this probability grows as we go to zero with q, which also means that some sub-groups and agents can get isolated, some of them left without any contacts, which will imply that these agents neither can influence nor be influenced by their environment, which will greatly hinder convergence of average statistics in several cases. Changing networks overcome this effect by shifting the network structure in every turn, thus there will be no constantly isolated agents; in fact, on time average all agents will have the same number of contacts, even in the probabilistic case. To make the above remarks on random networks a bit more exact, here is the distribution of the number of neighbors to an agent on a (probabilistic) random network:
⎛⎞P −1 kPk−1− Pr(# of Neighbors = k)=−⎜⎟qq (1 ) (3.10) ⎝⎠k
Here P is the population and q is the probability of the existence for any link connecting two agents. This is a binomial distribution, which is illustrated for convenience below for special values of P and q.
0.25
0.2
0.15
0.1
0.05
0 1 2 3 4 5 6 7
Figure 5 – Distribution of the number of neighbors on a (probabilistic) random network with SR=2, P=50 (therefore q=2/49)
As can be seen on this relatively scarce network there is a sizeable probability that an agent will be isolated, in line with what has been said above. I have to explain why I put the word ‘probabilistic’ into brackets. The reason is that even on a regular network when using
- 106 - the asymmetric type this will be the distribution of inverse contacts. 374 (On a probabilistic network neither the symmetry or asymmetry nor the directness or indirectness of contacts make a difference in this sense.) These differences between on the one hand the symmetric and asymmetric cases and on the other hand regular and probabilistic networks will have interesting implications in the following chapters. For example as we will see, a variable number of inverse connections can also influence dynamics when agents are able to punish because then some agents will get punished by more than others.
3.1.3. Compensating for Sight Range
The setup of the model implies that the various updating methods controlled by certain parameters are combined differently with the Sight Range. For example an agent can see SR (or SR+1 with CB_WUDS=1) central punishments, whereas SR(SR−1) (or SR2) peer punishments. The following table summarizes the different factors:
WUDC WUDP WUDC WUDP BUDP, Parameter BUDC, PPE, (Condition) CPE (CB_WUDS = 0) (CB_WUDS = 1) W
Factor SR SR(SR−1) SR+1 SR2 SR 1
Table 5 – SR factors
Knowing these factors is useful when we are trying to compensate for a change in SR. Modifying this parameter has two main effects. For example increasing it firstly gives more neighbors to the agents, immediately exacerbating peer effects, secondly, however, it also makes the network more connected facilitating information distribution and imitative transmission. When we would like to decouple these effects we can consider compensating for the more severe punishment in the parameters determining the severity of punishment (or possibly in W, if it is fixed). As it can be seen, a change in SR will usually entail a significantly stronger change in the effect of peer parameters than central ones. In the case of Watchfulness update SR is connected quadratically to WUDP, while only linearly to WUDC, while for Boldness and Reputation update linearly to BUDP and PPE and not at all to BUDC and CPE. While to a certain degree it is acceptable that a larger neighborhood will have a larger relative effect on people as compared to central effects, in some circumstances, especially when moving from a small neighborhood (low SR) to a much larger one (high SR) peer parameters could become overwhelmingly powerful relative to central ones. This is another reason why it is sometimes desirable to compensate for SR in the above parameters. There are at least two notable ways of compensation. The first, absolute compensation, counterweights the change in SR totally, separately for all parameters. In this
374 ‘Normal connections’ of an agent indicates those links through which an agent punishes and imitates other agents. ‘Inverse connections’ will be used to address those links through which an agent gets punished or imitated.
- 107 - case one should divide the parameter in question by the factor computed with the new SR and multiply it with the old one. For example for WUDP:
SR00(1) SR − WUDPcompensated= WUDP original (3.11) SR11(1) SR −
The compensated form of the rest of the parameters can be calculated analogously, using the formulas from Table 5. This way, with identical B and W levels, agents will have the same expected effects on B and W for the two SR level; the alterations in model dynamics will be due to the transformed network structure. (It must be added that although expected punishment will be the same after compensation, the two cases are still different in terms of certainty and severity.) The above method of compensation eliminates all direct changes in expected effects due to a change in SR. Nevertheless, it is also reasonable to assume that an increased number of connections will have a greater effect on the agent, and we only would like to avoid altering the relative strength of central and peer effects. To overcome this, it is also possible to compensate only one of them (either in a central or peer parameter) to adjust the change in expected effect to its counterpart (relative compensation). Let us consider how it can be done for WUDC and WUDP (with CB_WUDS=0). The relative SR factor of WUDP to WUDC can be acquired from Table 1 is
SR(1) SR − (3.12) SR
If we would like to keep this ratio at the same level when we change SR (from SR0 to SR1), we can compensate in WUDP the following way:
SR00(1) SR − SR1 WUDPcompensated= WUDP original (3.13) SR11(1) SR− SR 0
(We can also compensate in WUDC, only that we need to divide it with the above factor.) As it can be seen the first ratio is the same as the one in equation (3.11). Basically we have not done anything else but coupled the compensating factors of WUDP and WUDC and applied it only to one of them. The next table summarizes the factors to be used for absolute and relative compensation:
- 108 -
WUDC WUDP WUDC WUDP BUDP, Parameter BUDC, PPE, (Condition) CPE (CB_WUDS = 0) (CB_WUDS = 1) W Absolute SR SR(1) SR − SR +1 2 SR 0 00 0 SR0 0 Comp. 2 1 SR SR(1) SR − SR +1 SR SR Factor 1 11 1 1 1 Relative SR(1) SR − SR SR(1) SR − SR 2 2 SR SR 11 0 00 1 SR0 +1 SR1 SR1 +1 SR0 0 1 Comp. 2 2 SR(1) SR− SR SR(1) SR− SR SR+1 SR SR+1 SR SR SR Factor 00 1 11 0 10 01 1 0 Table 6 – Absolute and relative SR compensating factors
Naturally, on heterogeneous networks, parameters should be compensated individually, using the agent’s own SR (or the number of his inverse contacts in the asymmetric case.)
3.2. Rational Updating
As a starting point for demonstrating the model in action we consider a situation that resembles closely to classical models of Economics: agents are exclusively governed by rational maximization, they have perfect information, and the society lacks any enduring structure: agents are paired with each other randomly in each period. The upside of these strict restrictions is of course that we are able to produce analytical predictions, which in turn can be compared to the simulation output. This, on the one hand shows that analytical results can be reproduced using Contributron, and on the other hand it verifies the model. In this chapter we explore how discrete and continuous maximizing agents behave in different circumstances. First we examine how they respond to central punishment. Second, we turn to peer punishment and we compare their reactions on regular and probabilistic random networks, first for the discrete and in turn for the continuous case. In the meantime we demonstrate the correct functioning of the model by delivering analytical approximations, which we are able to do owing to the simple setup.
3.2.1. Central Punishment
The following two graphs correspond to probably the simplest arrangement the model is capable of:
- 109 - Mean Avg . Boldness vs . CPE Mean Avg . Boldness Mean Avg . Boldness vs . CPE Mean Avg . Boldness 1 1
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
CPE CPE -2 -1.5 -1 -0.5 -2 -1.5 -1 -0.5 Figure 6 – Mean Average Boldness at different levels of CPE with CPR=1, E=TR=1, BUR=1 and all other B and W updating parameters and PPE zero. Discrete (left) and continuous case (right).
What we can see on the left is that Mean Average Boldness375 (MAB) jumps at the critical CPE value from 0 to 1 just as it is expected considering the updating rule for BUR for the discrete case.376 The graph on the right corresponds to the continuous case, displaying a gradual change in MAB where the data points can be directly obtained by plugging CPE values into equation (2.3). As all connections between agents had been disabled by zeroing out PPE and all updating parameters except BUR, this picture is robust to all network arrangements. Moreover, as all agents face the same expected punishment all individual Bs are equal.
3.2.2. Peer Punishment
If we turn to peer punishment, the situation changes: allowing for heterogeous initialization of Watchfulness, depending on the mean W level of his neighborhood now all agents face different expected punishment which will make them choose different B levels. If we apply a fixed network, Bs will also be fixed at this level, but if we let the network change from period to period, we encounter more interesting results.
3.2.2.1. Discrete Case
For the discrete contribution case, and setting BUR=1 individual Bs will jump between 0 and 1 depending on the actual neighborhood of the agent. The type of randomization is also relevant: with regular networks agents will always have the same number of neighbors, which is why variation in expected punishment only comes from the level of W of the actual neighbors. Conversely, with probabilistic networks the number of neighbors is also variable, resulting in a higher variance in expected punishment and in turn in B. (Note that I have been using symmetric networks here, which is required for this result, as we are going to see.) Consider the following graph:
375 This title might be a bit confusing at first sight. Here ‘Average’ refers to a cross-section average while ‘Mean’ time average. Thus, this value is the grand (unweighed) average of Boldness for all agents and all periods (starting from the beginning of steady state, determined by the steadyStateStart variable in the Mathematica module. Wherever I use similar expressions it should be understand this way. 376 Notice that with a homogeneous population (in terms of E and TR) one can directly determine the average contribution from MAB using only the global parameters.
- 110 -
1
0.8
0.6
0.4
0.2
-0.25 -0.23 -0.21 -0.19 -0.17
Figure 7 – Simulated MAB (averaged over 100 runs) with discrete contribution at different PPE levels with probabilistic (red) and regular randomization (blue) and values from the corresponding analytical approximation (dark and light green, respectively).
The MAB here, as contrasted to the CPE case shows a gradual transition between 0 and 1, even with discrete contribution. The reason is that at a given level of PPE there will be agents who – by chance – are paired inversely with relatively low W (and/or fewer) agents and thus choose B=1 while others are connected to high W (and/or more) agents and consequently they will opt for B=0. Therefore, MAB is made up of the proportion of these two kinds of agents. As we raise PPE the probability of having a neighborhood which allows for B=1 decreases, thus MAB will get gradually closer to 0. We can also see how significant the difference is between probabilistic and regular randomization. The reason for this is better explained by looking at the analytical approximation of the two situations. Let us start with the regular case, which is somewhat easier to obtain. What we need is the expected fraction of agents with a neighborhood of average W lower than the corresponding break-even level at any given PPE. Because the simulations above used a neighborhood of 10 for all agents (in a population of 20) and E=TR=1, this level is given by Wbreak_even=−1/(10*PPE). In other words if an agent is put in a neighborhood where the average W is this high his expected income from shirking is just 0. The reader can check that at PPE=−0.2 this level is 0.5, which is the mean of all Ws in this simulation (W was initialized with a uniform distribution between 0.25 and 0.75 and was kept fixed for all agents), therefore MAB=0.5, since then on average half of the agents will be in an environment where average W is greater and half of them where it is lower than the break- even level. To be able to tell this ratio for all possible PPE levels, we need the distribution of average W in a neighborhood of 10 with the above initialization for W. Using the Central Limit Theorem, it is possible to approximate this with a normal distribution of mean 0.5 and 2 1/2 2 standard deviation (σu(0.5) /10) , where σu(0.5) is the variance of a uniformly distributed random variable of range 0.5 (e.g. between 0.25 and 0.75), which is 0.02083·. By plotting the value of the corresponding CDF for average W values transformed from PPE with the
- 111 - formula for the break-even level we get the light green line in the above graph. What it says is that at the given PPE level on average this fraction of the agents will be in a neighborhood where the average W is smaller than the break-even level, consequently this is the expected ration of agents with B=1 and B=0, and thus it is also the expected value of MAB. The small remaining discrepancy between this and the blue line results from the approximation we made for the distribution of average W. The analytical solution for the probabilistic case can be obtained similarly, only the approximation for the distribution of W levels in a neighborhood is a bit trickier to get as we need to consider the effect of the variable number of neighbors. What we need here is not the distribution of average W in a neighborhood as it does not tell us anything about the number of neighbors and thus expected punishment, but the distribution of sum W/SR.377 Knowing this we are able to tell the expected punishment an agent faces at any PPE level and thus the fraction of agents with B=1 at that particular level. (In the previous case these two things were essentially the same, since all agents had the same number of neighbors in all periods.) The PDF of the distribution in question is given by
kPk−−1 P−1 ⎛⎞P −1 ⎛⎞⎛⎞SR SR PDFW () x =−∑⎜⎟ *⎜⎟⎜⎟ *1 * k=1 ⎝⎠k ⎝⎠⎝⎠PP−−11 (3.14)
*(*)*PDF21/2 x SR SR Normal( k *0.5,(σu (0.5) * k ) )
(P is the total number of agents in the population and SR is the expected number of neighbors.) The resulting approximation for MAB, that is the corresponding CDF at −1/SR*PPE with SR=10 and P=20 is plotted above as the dark green line (very close to the simulated red one).
3.2.2.2. Continuous Case
If we move to the continuous case it might be curious at first sight that we do not find such a difference between the two kinds of randomization as above. The left part of the figure below shows what we encounter here in terms of MAB transition, while the right part will help us in understanding the discrepancy with the preceding case:
377 While we could use simply the distribution of sum W, dividing it with SR will allow us to compare this distribution with that of average W with regular randomization.
- 112 - -0.325 -0.275 -0.225 -0.175 -0.125 -0.075 8 0.9
0.8 6
0.7
0.6 4
0.5 2 0.4
0.3 0.2 0.4 0.6 0.8 1
Figure 8 – Simulated MAB levels at different PPE values with continuous contribution and probabilistic (red) and regular (blue) randomization (left) and the PDF of sum W/SR in the probabilistic (red) and regular (blue) case (right).
As we have seen sum W/SR has a higher standard deviation with probabilistic randomization because of the variable number of neighbors. This difference is conveniently depicted on the right part of the above figure. But why does not this cause a higher disparity between the MAB levels of the two kinds of randomization with continuous contribution as well? We can find the answer by taking a better look at the figure on the right above. In the discrete case we have used the corresponding CDFs of the above PDFs to obtain the MAB level at different PPE levels because MAB was practically the same as the ratio between agents with B=1 and B=0. Obviously, these CDFs are rather different at certain values. On the contrary, to get an analytical prediction for the MAB level in the continuous case we only have to use the mean of these distributions, as each agent is capable of setting his B individually at the optimal level. Of course the variance of the individual Bs (and therefore MAB’s) will be still higher in the probabilistic case, which however, does not interfere with the mean. Therefore, as the two distributions have approximately the same mean, simulated MABs will also be close. Observe, though, that there is still a small difference between the two lines. This is due to that the higher variance of the expected punishment on the probabilistic network still affects MAB through the curvature of the optimal B. Considering Figure 6, it is not difficult to imagine that a higher variance of expected punishment (which on that figure only depended upon CPE, but now it is determined by the composition of the neighborhood) on average causes a higher optimal B, therefore higher defection even with the same mean punishment. This is the case at high punishment levels, resulting in a higher MAB on a probabilistic network, but at low PPE levels (close to zero) it is the other way around. When PPE’s value is low the level of B is generally high, therefore when the actual optimum is low it will pull down B more vigorously simply because it is farther from this actual low target value. (This also implies that there is a special PPE level, where the two networks have the same punishment effectivity.)
3.2.3. Distribution of Neighbors
I have mentioned that using symmetric networks is necessary to get the above results. It comes from the fact that when this is relaxed agents will have the same distribution of number of inverse neighbors both on probabilistic and regular networks. (As can be seen from
- 113 - the explanation of equation (3.10).) However, dynamics of the two cases, regular and probabilistic networks, can still differ in the asymmetric case, too, since we always have similar discrepancy between the distributions of the number of direct connections.
3.2.4. Summary of Findings
● Contributron is capable of modeling situations set up by using classical economic assumptions: maximizing agents, perfect information and no social structure. It reproduces the analytical predictions, which verifies the model. In addition we have seen how simulation output can induce analytical insight (with the random network behavior).
● With central punishment all agents face the same expected punishment, therefore in this homogeneous population of maximizers each agent has the same propensity to defect. In the discrete contribution case average contribution jumps from 0 to total where expected punishment equals the amount to be contributed, while in the continuous case we observe a gradual transition.
● Even in the discrete case, a scheme with peer punishment shows a gradual transition in the average contribution (defection) level because it depends upon the ratio between the number of agents facing an expected punishment higher and lower than the critical value.
● With discrete contribution, on a probabilistic network the transition of average contribution is significantly longer than on a symmetric regular one, because expected punishment has a larger variance owing to the variable number of inverse contacts.
● With continuous contribution, we do not find a comparably serious difference between the contributions on regular and probabilistic networks, since in this case the overall contribution depends mainly on the mean of the distribution of expected punishment, as opposed to the discrete case where it is much more strongly influenced by the variance.
● With continuous contribution the variance of expected punishment still has an effect on the average contributions but only through the curvature of the optimal defection level. With a severe punishment it results in a higher, with a weak punishment a lower mean average defection level for a random probabilistic network than for the corresponding regular one.
● The distribution of inverse contacts are the same (binomial) in the probabilistic and asymmetric regular random networks, entailing that agents face the same distribution of expected punishment as opposed to the symmetric case. When peer punishment is present this is what causes the discrepancy between the behaviors of the two network types in the symmetric case, but does not do so in the asymmetric case.
- 114 - Naturally, these findings represent only a small fraction of what the model is possibly capable of in the same fashion with some further complications.
3.3. Imitative transmission
To portray the social updating mechanism, I have selected a topic that has already been touched upon in the literature review. It has been stated that in certain circumstances, especially in noisy and complex environments where either information is expensive or deriving the optimal strategy from it is difficult, imitation can be the optimal strategy for boundedly rational actors. The argument in brief is that imitation is effectively a short-cut on search-costs by utilizing the information processing already achieved by other members of the population (or recognizing the result of a selection process operating on the population, which will be the case here). In this chapter first I will demonstrate how my simulated agents are capable to get to the optimal defection level only by selectively copying strategies. Next, we turn to investigating what conditions allow for this. To start with we examine the relevance of network structure. Then realizing that in certain circumstances populations tend to run past the optimum, we focus on and three parameters: the attenuation of Reputation, RA, the noise in Boldness, BUND and the certainty of central punishment, CPR and their interactions. Finally we look at how imitative transmission perform as we change the quality of imitation from payoff-biased to average-biased.
3.3.1. Emergence of Optimum
The following graph displays a situation where agents sweep to the optimum without using their rational updating mechanism (BUR=0), but being driven by payoff-biased imitation towards only the most successful agent in their neighborhood (BUS=0.01, BUSC=0).
Plot of Avg . Boldness 0.85
0.8
0.75
0.7
0.65
800 1600 2400 3200 4000 0.55
Figure 9 – Average Boldness converging to the optimal level (0.833) with BUR=0, BUS=0.01, BUSC=0.
We had CPR=0.3, CPE=−2.0, and PPE=0, from which using the formula for BUR with continuous contribution (equation (2.3)) the optimal level of B can be quickly obtained, Bm=0.833. The AB reaches this value quite quickly. In this special case B was initialized with RNDU(0,1), the default initialization, for which it is likely that there are agents already at the
- 115 - startup whose B is close to the optimal level. This facilitates the attainment of optimum for the rest of the agents. Nevertheless, in most what is follows, I have initialized B with 0.5 for all agents, and as we will see, at least with a reasonable level of noise added to it, the population still easily hits the optimum.378
3.3.2. Determinants of Convergence
Of course, there are numerous candidates among the parameters and settings that are likely to influence the course of this convergence. In this section we are going to explore the most important factors: the network structure, the discount factor, the noise and the certainty of punishment.
3.3.2.1. Network Structure
The first of them that comes into mind is network structure: it is quite intuitive that in a situation where information spreads through a network by imitation, the structure of the network will substantially alter the behavior of the system.
3000
2500
2000
1500
1000
500
RCOR RCOP RCHR RCHP RING LINE
Figure 10 – Periods needed to reach AB=0.8 when the optimum is 0.833 from default initialization on different networks with SR=2 (red columns (left)) and SR=10 (blue columns (right)) (P=50, 10 runs)
This statistic tends to differ between networks much more seriously when SR is low. This is quite natural, as we raise SR, all networks converge towards full connectivity that is they become more similar to each other. Observe also that agents generally tend to converge
378 The following bit, the exploration of the effect of network structure, has also been carried out with the default initialization.
- 116 - faster when they are more connected. This again seems rather trivial, but in the chapter on network heterogeneity we will see that this can be a more involved question. When SR is low the most spectacular outlier is RCOP. If we refer back to what has been said about network connectivity, it is not very hard to find the reason. With SR as low as 2 there are many isolated agents and sub networks which greatly hinders overall convergence. Unconnected agents are unable to select between strategies, they just follow a random walk (when BUND>0). Consequently either the rest of the population must reach a significantly better convergence or they must wait until the isolated agent wanders towards the optimum by chance before the population average B can reach the required threshold. As SR grows, the probability of complete isolation quickly diminishes, this is why the great improvement in the performance of RCOP between SR=2 and 10. On the contrary, with RCOR, although the average number of connections is the same, there are no isolated agents, and this is why it does not need a long time for convergence. On RCHP, isolation occurs only for certain turns, which is quickly resolved by re-randomization. Check also how RING and LINE relate to each other and the random networks with a low SR. It is another manifestation of the relationship between these networks’ connectivity. Remember that LINE has the lowest, RING a mediocre and random networks the highest connectivity in terms of average link length between two randomly selected agents. Accordingly, we find the same order in the speed of convergence: LINE being the slowest, RING moderate and all random networks quite close to each other except for RCOP for the above described reasons.
3.3.2.2. The Discount Factor, Noise and Certainty of Punishment
The network structure, however, is far from being the sole factor that influences imitative convergence. We find that there are at least three very important parameters in this respect: the discount factor, RA, the noise involved in B, BUND, and the certainty of punishment, CPR.
3.3.2.2.1. A Curious Phenomenon
Interestingly, with a low RA, BUND or CPR setting, we often find the following:
Plot of Avg . Boldness Plot of Avg . Reputation
10000 20000 30000 40000 50000
0.82 0.9
10000 20000 30000 40000 50000 0.8
0.78
0.7 0.76
0.6 0.74
Figure 11 – Average Boldness and Reputation with RA=0.5, BUND=0.005, BUS=0.1 and BUSC=0
- 117 -
Here we have used the payoff-biased updating method much the same way as above. However, for some reason the B still overshoots the optimum which is clearly reflected in the Reputation level. (Observe though the small landing in AB near the optimum.) What could go wrong here? To understand what causes this we should first consider what a low level of RA implies. It makes the consequences of past behavior become insignificant relatively to more recent events, in other words it makes the agents have a short memory. Thus, if agents are using payoff-biased updating, their decisions will mainly be based on the outcome of recent actions. Then agents do not choose basing on the long run average success of strategies; if past is discounted away agents will generally copy those who do better most often. This way if punishment is uncertain, even if it is severe, those with a higher propensity to defect will be imitated most often. On the other hand if there are only small differences between strategies (B), due to the randomness of shirking and getting caught, it generally takes a longer time until these differences translate into success as measured by R, and the more so the more uncertain the punishment is. 379 Thus, noise that is capable to pull strategies apart has an important role in the emergence of the optimal defection level. Due to a relatively low380 BUND, agents were also quite close to each other in terms of B:
Plot of Indv . Boldness Plot of Indv . Reputation
10000 20000 30000 40000 50000
0.9 0.85
0.8 0.8
0.7 0.75
0.6
10000 20000 30000 40000 50000
Figure 12 – Individual Boldness and Reputation for the same situation as in Figure 11
In such a situation agents with a slightly higher B than their neighbors will do better most of the time, and the gap between B levels is not big enough for R to signal the right long term income difference between strategies before it is discounted away by RA. Considering what has been said in the previous paragraph, agents will copy most of the time neighbors with a higher B until B runs past the optimum and hits the ceiling, deteriorating R levels.
3.3.2.2.2. The Effects and Interaction of Parameters
379 Note that here I have used a high CPR which has two main advantages. Firstly there is less noise in R, which allows us to see how it drops back as B overshoots the optimum, secondly it makes easier the investigation of the effects of RA and BUND. (Refer to Figure 14: with a low CPR RA hardly has an effect in the range.) Overshooting can occur with high CPR, too, because punishment is still uncertain considering that the probability of getting caught is proportional to B. How high and low certainty scenarios relate to each other is analyzed later in this chapter. 380 Should be measured to BUS, which pulls the agents together.
- 118 - There are at least three ways to overcome this effect. The first is of course to make RA higher to prevent disappearance of past outcomes too early. The second is to introduce a reasonable level of noise (BUND) to make individual Bs go apart entailing that on average less periods are needed before the difference between strategies manifest in R so that agents can distinguish between strategies even with a smaller RA. The third is to make punishment more certain. The following graphs show how different RA and BUND levels affect MAB.
Mean Avg . Boldness Mean Avg . Boldness vs . RA Mean Avg . Boldness Mean Avg . Boldness vs . BUND RA BUND 0.545 0.55 0.555 0.56 0.0076 0.0078 0.008 0.0082 0.0084 0.975 0.975
0.95 0.95 0.925 0.925 0.9 0.9 0.875
0.875 0.85
0.85 0.825
0.825 0.8
Figure 13 – Drop of Mean Average Boldness levels in response to raising RA an BUND.
There is a rather sharply determined value of both parameters separating domains where MAB can converge to the optimum and where it can not. Moreover these values are interrelated: with a higher BUNM agents are able to get to the proximity of the optimum even with smaller RA, and a higher RA allows for lower BUND. The following experiment illustrates this cross-effect.
Mean Avg . Boldness vs . RA for different values of BUND Mean Avg . Boldness BUND = Mean Avg . Boldness vs . RA and BUND 0.007 0.008 0.95 0.009 0.01 0.011 0.012 0.9 0.013 0.014 0.015 0.85 0.016
RA 0.95 0.42 0.44 0.46 0.48 0.5
0.0077 0.90 0.008.008 0.850. Mean Avg . Boldness Mean Avg . Boldness vs . BUND for different values of RA 0.009 Mean Avg . Boldness 0.01 0.80.8 0.5 RA = 0.011 0.49 0.4 0.48 0.41 BUND 0.012 0.47 0.95 0.42 0.013 0.46 0.43 0.45 0.44 0.44 0.45 0.014 RA 0.9 0.46 0.43 0.47 0.015 0.42 0.48 0.41 0.49 0.016 0.4 0.85 0.5
BUND 0.008 0.012 0.014 0.016
Figure 14 – Cross-effect between the critical values for BUND and RA allowing for attainment of optimal strategy by payoff-biased imitation
(Note also how the slope of the transition becomes shallower at high values of BUND and low values of RA: the noise drives MAB from the extreme towards 0.5)
- 119 - Nevertheless, while a moderate noise added to B seems to benefit evolution, we expect that too much will impede getting to the optimum again. Indeed, the following figure shows that there is an optimal level of noise below which either there is not enough variation in B to reach the optimum early enough or closely knit B drives MAB past the optimum. On the contrary, a high noise level overwhelms everything else and drives MAB to 0.5 again.
Mean Avg . Boldness Effect of Noise on Attaining Optimum by Payoff −biased Imitation
0.8
0.75
0.7
0.65
BUND 0.001 0.006 0.01 0.06 0.1 0.6
0.55
Figure 15 – MAB at different BUND levels. (Note that the horizontal axis is not linear. Optimal B is 0.833)
Let us finally consider how different certainty-severity configurations (with equal expected punishment) influence convergence.
Mean Avg . Boldness vs . CPR and CPE constant product at different levels of RA
Mean Avg . Boldness vs . CPE Mean Avg . Boldness CPE -50 -40 -30 -20 -10 0.975
0.95
0.925 0.95
0.99 0.10.1 0.9 Mean Avg . Boldness 0.8585 0.3 0.875 0.1 0.2
0.3 0.5 0.85 0.4 RA 0.5 0.825 CPR CPE 0.6 0.7 0.7 0.8 ê 0.8
0.9 0.9
Figure 16 – MAB levels with constant CPR*CPE, (moving CPR from 0.1 to 0.9 and compensating CPE accordingly) on the left axis and different levels of RA on the right axis (left); reaction of MAB to CPE with CPR=0.1 (right).
On the left we can see that moving CPR towards 1 while keeping CPR*CPE constant helps the population to reach the optimal B level, in other words the overshooting occurs more easily with low certainty punishment schemes. We can also see the interaction of different certainty-severity pairs with RA. (With a low RA even a high CPR cannot make MAB depart from close to 1. Conversely, with a low CPR RA hardly has an effect on MAB.)
- 120 - On the right we see that with CPR=0.1 (a low value) we need to raise CPE (in absolute value) dramatically to reach the once optimal level in B, which is easily achieved when CPR is high. For example we need CPE=−50 to get close to MAB=0.833, which makes CPR*CPE=−5, while the same level of MAB can be reached with only CPE=−0.6 when CPR=1 (CPR*CPE=−0.6, which implies a much lower expected punishment).381 That a low CPR hinders convergence conjures up the debate on the primacy of certainty and severity. Indeed, we can see that when agents are governed by rational maximization (BUR), only the product CPR*CPE is considered in the formulas for optimal B, therefore for these agents there is no difference whether we use a severe but uncertain or frequent but weak regime. (There can be a difference in terms of costliness, but it is exogenous for the model. It can still be considered, though, as a policy issue.) However, if we are willing to accept that agents are not chemically pure individual maximizers, but they tend to imitate, the difference between the above two cases becomes important immediately. As demonstrated, a low CPR can be less effective in suppressing defection. We can try to counterweigh this by raising CPE, but with a low certainty it requires substantially more severe punishment to reach the same level in B than with a higher certainty. Note that here the inefficiency of low probability punishment comes purely from the effect of discounting Reputation and has nothing to do with the expressive function of law and peer pressure. (Which connection will be shown later.) These are two different phenomena both pointing towards the necessity of a more certain central punishment scheme
3.3.3. Payoff and Average-Biased Imitation
Since this chapter is devoted to imitative updating, I need to mention majority-biased transmission. To connect it to the payoff-biased mechanism let me present here an example where we move BUSC between 0 and 1, thus gradually transforming the members of the population from payoff-biased to average-biased imitators.
Last Avg . Boldness vs . BUSC for different values of G Mean Avg . Boldness Mean Avg . Boldness vs . BUSC Last Avg . Boldness BUSC 0. 0.2 0.4 0.6 0.8 1. G = 0.8 1000 2000 0.9 3000 0.75 4000 5000 6000 0.8 0.7 7000 8000 9000 0.65 10000 0.7 20000 30000 0.6 40000 0.6 50000 0.55
0.5 BUSC 0.2 0.4 0.6 0.8 1
0.4
Figure 17 – MAB levels with different BUSC settings. (Optimal B=0.833, SR=5, BUND=0.005) (left); Convergence profile (MAB after 1000, 2000, …, 10000, 20000, … 50000 periods.) at different BUSC levels (right)
As expected, a lower BUSC (payoff-biased transmission) drags MAB closer to the optimum, whereas a higher BUSC leaves it around the initial 0.5. What is noteworthy is the
381.
- 121 - sharp drop around BUSC=0.5 (linear interpolation in weights from the most to the least successful neighbors) above which convergence seems much weaker than below even if we let the simulation run for very long. Observe also the shrinkage of the confidence band of MAB as agents get more payoff-biased and begin to select between strategies instead of just blindly incorporating into their strategies every variation that occur in their neighborhood. Note also that even with BUSC=0 the MAB stays slightly under the optimum. This is the effect of the noise in accordance with our discussion on the nature of BUND. On the right we can also have an impression on the speed of the convergence process at different BUSC levels.
3.3.4. Summary of Findings
Even though it has been only a short analysis of imitative transmission of strategies that concentrated on a few specially selected parameters and conditions, there are a number of lessons and predictions that we can learn from this chapter:
● In effect, payoff-biased imitation is able to mimic outright maximization − when circumstances are favorable, evolution can reproduce deliberate optimization, and optimal defection levels can emerge.
● Sparse social networks and the lack of small-world connections may effectively hinder information spreading and thus attainment of optimal strategies.
● When payoffs are volatile in time, payoff-biased transmission may miss the optimum if agents have a short-term memory, punishment is uncertain and if there is not enough diversity in propensity to defect.
● A moderate level of noise in strategy replication and a sufficiently high discount factor may facilitate the attainment of optimal strategies. These values mutually depend on the level of the other.
● With imitative agents certainty of punishment becomes more important than severity: low certainty - high severity punishment schemes are less effective than high certainty - low severity ones.
● Already a moderate bias in imitation towards successful outcomes can be effective in governing populations to the optimal strategy.
Naturally, the analysis undertaken in this chapter is limited. There are far more possible parameters, parameter combinations and other settings already in the model that can have an effect on the discussed phenomena and induce others.
3.4. Direct Effects
- 122 - Direct effects in Contributron are those that directly connect punishment to changes in B and W. They are controlled by four parameters BUDC, BUDP, WUDC and WUDP. While having considered their mechanism in model description they might seem at first sight to be the simplest of the various updating mechanisms, we will see that they are capable to generate surprising effects. In this chapter following the description of the basic characteristics of direct effects I am going to concentrate on two of the more involved phenomena related to them: norm cascades and oscillations. For norm cascades after demonstrating their occurrence in Contributron and explaining the relevance of direct effects in this respect, we derive the so- called ‘Ignition level’ of Watchfulness which is important to understand how norm cascades come about in the model. Next we examine the role of chance events and finally we present an example that demonstrates how seemingly stable cooperation schemes can suddenly collapse. Then we move to oscillations: joint movements of norm adherence up and down. After showing the basic mechanism we compute a number of necessary conditions for oscillatory dynamics. In turn we investigate how capping Watchfulness levels gives rise to a continuous type of oscillation, and we will also learn about the special connection between direct effects and oscillations. Before the conclusions we will see some more setups that exhibit oscillatory dynamics without direct effects.
3.4.1. Basic Features
The figure below illustrates how AB and individual Bs fall off when using only direct effects to update B while keeping W fixed.
Plot of Indv . Boldness Plot of Avg . Boldness
0.3 0.8 0.25 0.6 0.2
0.15 0.4
500 1000 1500 2000 2500 3000 3500 4000 0.2 0.05
800 1600 2400 3200 4000
Figure 18 – Average Boldness (left) and Individual Boldnesses (right) going to 0 at a geometrical rate when governed by BUDC (=−0.03, left) and BUDP (=−0.0015 with SR=2 on a RCOR network, right)
In this situation Average Boldness has an easily calculable half-life382:
382 To be correct, this is the expected value of the half-life for two reasons. Firstly, it is due to the stochasticity of punishment and shirking, which, however, on larger populations should be close to the actual one. Secondly, when BUDP≠0 each agent can have a different rate of change in B depending on the number of his punishing neighbors and their Ws − and it is of course not indifferent if high or low B agents have a faster rate when it comes to computing the average.
- 123 - ln(1/ 2) N = , (3.15) AB_ Half− life ln(1++CPR * BUDC W * SR * BUDP )
where W bar is the population average W. If we combine direct effects with other updating mechanisms we find that AB level tends to stabilize at specific values. This equilibrium level can also be determined without much ado. If the rate of change due to the other updating mechanism depends on the level of B, like in the case of BUR, having a stronger effect when B is farther from the target, the equilibrium level for AB is given by:
BUW* B B = T , (3.16) Stable,Target BUW−− CPR*** BUDC W SR BUDP
where BUW is the corresponding weigh of the other effect (e.g. BUR), and BT is the target value of that effect. However, when the other effect is an unconditional one, independent of the level, (like BUNM), the stability sets in at:
BUC BStable,Uncnd = , (3.17) CPR*** BUDC+ W SR BUDP
where BUC is the per period rate of change due to the other effect (e.g. BUNM) . The following pictures show B stabilizing as a result of being driven jointly by a direct and another effect.
Plot of Indv . Boldness Plot of Indv . Boldness 0.9
0.8 0.6
0.7
0.5 0.6
0.5 0.4
0.4
2000 4000 6000 8000 10000 4000 8000 12000 16000 20000 BUR=0.001, BUDC=−0.003, CPR=0.3, BUDP=0 BUNM=0.0006, BUDC=−0.003, CPR=0.3, BUDP=0 BT=0.833, BStable,Target=0.438, MAB=0.439 BStable,Direct=0.666, MAB=0.662
Figure 19 – Boldness stabilizing at the theoretical level due to being driven by BUDC and BUR (left) and BUNM (right)
3.4.2. Norm Cascades
- 124 - In the first part we have discussed in detail generalized increasing returns, positive feedback, and their manifestation in norm change, norm cascades. We have emphasized that norm cascades is a characteristic feature of norm dynamics. A norm cascade is a long period of high or low level of norm penetration in society (high or low AW or AB), followed by a sudden transition into the opposite extreme. The direct effects of Contributron have been designed to be able to reproduce this kind of phenomena. Consider the following figure.
0.06 0.2
0.055 0.175
0.05 0.15
0.045 0.125
0.04
10000 20000 30000 40000 50000 0.035 0.075 0.03 0.05 0.025
0.025
Figure 20 – Positive feedback in AW (left) and individual Ws (right) triggering norm cascades. (The corresponding AB graph can be found in Figure 26.)
The intuition behind what is happening here is easy to understand. WUDP being greater than 0, peer punishment is generating more peer punishment by raising W each time an agent sees his neighbors punishing. (The real-world analogy is that to see other people punish encourages one to follow their practice: it is easier to join in punishing that to be the first to do so.) Until W is below a certain level, a downward drift (e.g. by recognizing that to punish is costly) can be strong enough to keep W down, but reaching a certain point this positive feedback in W becomes strong enough to shoot punishment upwards. This threshold level of W depends on several factors.
3.4.2.1. The Ignition Level
Supposing that seeing punishment facilitates becoming a punisher,383 there is a special level of Watchfulness where its expected change is zero.
3.4.2.1.1. The Derivation and Relevance of Ignition Level
For a particular agent i, we have the following equation where the expected change in his W is zero:
2 Bii(*CPR WUDC+=− SR ** W WUDP ) WUNM (3.18)
383 And also that without it W goes down.
- 125 - Rearranging this equation, we can get a formula for the average W level in an agent’s neighborhood, where his W is expected to be stationary:
* WUNM+ Bi ** CPR WUDC Wi =− 2 (3.19) BSRWUDPii**
I am going to call this value the ‘ignition level’ of W.384 From this formula it is easy to see the partial effect of each component on the ignition level, all of them are quite reasonable. For example a higher CPR makes it easier for the local punishment to ignite by lowering the ignition level. A higher B level also reduces it, and so on. Although this boundary seems to be a strict one, because of the stochastic nature of the model and the structured social network the picture is not so clear. For example considering the parameter settings chosen for producing Figure 20 (WUDP=0.01, WUNM=−0.002, SR=2) and the AB at the point where W was ignited (approximately 0.683) the ignition level for the above situation (calculated with AB) is about 0.0732. We can see on the above graph that the average W level is nowhere near it where it suddenly begins to increase. The reason is that if a small sub-population of agents is able to reach the ignition level (their ignition level, to be correct), their W begins to grow, and provided they are connected to the rest of the population, they will make it easier for the remaining part of the agents to reach their threshold, igniting a chain reaction of exploding W. Examining the right hand side of the graph above we can see that before the W begins its take-off, there are certain agents jumping slightly above the approximate ignition level, without being able actually ignite W. (Presumably because their local B is not high enough yet, thus their ignition level is still higher.) Then finally a subgroup crosses its local ignition level, and begins a sudden W ascent, pulling the rest of the population with themselves. (What suggests that it is a subgroup is that AW is much lower than peak agents’ W before the jump. See also the grids of a norm cascade in B on Figure 25 clearly showing the local source of a norm cascade.)
3.4.2.1.2. Chance Events and the Attainment of Ignition Level
But there is still more to the story. So far we have seen the consequence of the relative isolation of sub-groups being able to generate ignition level condition locally that spreads out in the population. The other important factor here is that even without having a B level that is close to the one that is able to support a W close to the ignition level, just by chance W is able to reach ignition level if we wait long enough. There are two major sources for this kind of chance. Take a look at the graphs below.
384 Note that using SR2 implies that we use CB_WUDS=1 in simulations. When CB_WUDS=1, SR2 should be substituted with SR(SR−1) in the above equations. Note that also all agents have an individual ignition level. Sometimes, however, I speak about the ignition level in a population, where I understand a value calculated using the same formula, but inserting AB instead of individual Bs, and the global SR. It is of course only an approximation, but in closely tied populations it is close to the individual values, and gives a clue about where AW is expected to ignite. (Populations displaying norm cascades and oscillations are likely to be closely tied in terms of norm adherence right because cascading agents pull their peers with themselves, thus the whole population tends to move together.) Also, for simplicity at many places I am talking about how B or W moves, where I understand AB or AW. When agents move closely together, for example because W outbursts are synchronizing the population as mentioned, average and individual levels are also close to each other anyway.
- 126 - Period Periods to Reach Ignition Level W Period Periods to Reach Ignition Level W 25000 12000
AW AW 10000 20000
8000 Individual Individual 15000 6000
4000 10000
2000 5000 B Level 0.625 0.65 0.675 0.7 0.725 0.75 Ignition Level W 0.08 0.07692 0.074 0.071428 0.06896 0.06 WUND J N 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 J N J N J N J NJ N J N H L Figure 21 – Average number of periods needed for AW and individual Ws to reach ignition level with WMIN=0.03, at different levels of B (left) and WUND (right)
The first kind of chance events that helps W to reach the ignition level comes from the randomness of getting caught. If an agent shirks more often and/or his peers or the central authority checks him more frequently just by chance it might happen that his W will reach a higher level than ex ante expected. Of course the longer we wait the more probable it becomes that unlikely events occur, more specially the longer we wait the higher W will appear in the population of a given B. On the left graph above we can see the average number of periods needed for AW and the agents to reach the ignition level W at different levels of B. What we find is that the higher is B the fewer periods it takes. (On the one hand because ignition level is lower, and on the other hand because a higher B ceteris paribus implies more frequent punishment, which implies faster ascendance of W under the ignition level.) The right part of the figure depicts a similar relationship, only this time we have WUND on the horizontal axis, the second source of randomness, noise. Thus, as we would expect, having a noise in W of higher standard deviation makes it easier to reach the ignition level. WUNM and WUDP influence the speed W and AW reaches the threshold similarly to B: on the one hand they move the ignition level as determined by equation (3.19), and on the other hand they alter the rate of change in W. Unlike B, however, WUDP does not influence W through changing the frequency of punishment, but its magnitude, while WUNM works by just modifying the drift. The following graphs illustrate this relationship.
Period of MAW reaching Ignition Point Period of MAW reaching Ignition Point vs . WUNM0 and WUNM1 Period of MAW reaching Ignition Point Period of MAW reaching Ignition Point vs . WUDP
70000 20000
60000
15000 50000
40000
10000
30000
20000 5000
10000
WUNM0 WUNM1 WUDP −0.0019 −0.0018 −0.0017 −0.0016 −0.0015 −0.0014 −0.0019 −0.0018 −0.0017 −0.0016 −0.0015 −0.0014 0.0093 0.0094 0.0095 0.0096 0.0097 0.0098 0.0099 0.01 J N J N J N J N J N J N J N
Figure 22 – Average number of periods needed for AW to reach ignition level with different values of WUNM0=WUNM1 (left) and WUDP (right)
- 127 - Note that W was bound below by WMIN at 0.03 in all these experiments. It was necessary, because without other effects in W if we leave W to die out, there is no peer punishment any more, thus W will be permanently locked at 0. This ‘norm trap’ can be prevented by setting a floor for W with WMIN (which is quite natural considering what has been said in the first part about people’s natural willingness to punish defectors) or setting WUDC>0 with CPR>0 representing the expressive function of law. (Adding a noise even without a drift can also suffice.) The values of WMIN, CPR and WUDC, of course, have also a great influence on the average number of periods needed to ignite W.
Period of MAW reaching Ignition Point Period of MAW reaching Ignition Point Period of MAW reaching Ignition Point vs . WMIN Period of MAW reaching Ignition Point vs . CPR
15000 17500
15000 12500
12500 10000
10000 7500
7500
5000 5000
2500 2500
WMIN CPR 0.026 0.02675 0.0275 0.02825 0.029 0.02975 0.29 0.3025 0.315 0.3275 0.34
Figure 23 − Average number of periods needed for AW to reach ignition level with different values of WMIN (left) and CPR (right)
All the graphs of the above three figures show the number of periods necessary for AW to reach ignition level only along a one dimensional grid. Since all these parameters influence this statistics simultaneously, we would need a grid of many dimensions to have the whole picture. This, however, is certainly a task beyond the scope of this chapter and it would require a heavier computing power that I have access to. Nevertheless, what has been done is enough to convincingly demonstrate the effect of the parameters in this respect, besides the statistic is easily obtained for any parameter combination of interest by running the model just a few times if necessary.
3.4.2.2. Breakdown of Coopearation
Although I have chosen the positive feedback in W for a deeper insight into norm cascades because it leads us to our following topic, oscillations, B can also show similar phenomena in the model through slightly different mechanisms: cooperation can also break- down suddenly.
- 128 - Norm Cascade − Breakdown of Cooperation 1
0.8
Boldness 0.6
0.4 Wtchfness
0.2
10000 20000 30000 40000
Figure 24 – Breakdown of cooperation: average Boldness and Watchfulness inverts suddenly following a long period of low defection
This cascade was induced by a negative WUR. In other words we have supposed here that agents who are not willing to cooperate will also be less likely to punish defectors. In addition, we have kept our assumption that willingness to punish is supported by seeing others punishing that is WUDP>0. For a long time B and W were in a seemingly stable equilibrium, until chance events were able to topple the first domino. The figures below help us better understand how this transition took place.
Boldness Watchfulness 0 0 0 0
9000 9000 9000 9000
18000 18000 18000 18000
27000 27000 27000 27000
36000 36000 36000 36000
45000 45000 45000 45000 0 20 40 60 80 100 0 20 40 60 80 100
Figure 25 – Grids of a norm cascade on a RING network (SR=2)
Thanks to the special network chosen, we can see that the whole process has begun at one particular location. Because I have used a RING network, the course of events is easy to follow, although the essence of the things is the same on other structures, too. Because of stochastic events385 an agent’s W gets under a critical level, therefore his neighbors get less punishment, therefore WUDP will be less able to keep up their W, which also begins to move
385 Observe that even while W is still high and B low there is perceptible fluctuation in them.
- 129 - downwards. This leads to an increasing B of the original agent, which through WUR further weakens his W and in turn his neighbors’ W. This way if an agent’s W begins to fall, it will endorse a fall in his neighbor’s W, and the process quickly undermines cooperation in the whole population. The nature of change, thus, is essentially similar to what we have discussed above in connection with cascading W.
3.4.3. Oscillations
The final section of this chapter is oscillations. Oscillations in Contributron are not exclusively coupled with direct effects. In fact this topic appears to be so rich in itself that one could fill a whole book with it. However, direct effects are specially connected to them right because of the already highlighted positive feedback property. In the remaining part of this chapter I will demonstrate how the feedback and norm cascades can generate a special, non- attenuating type of oscillation. I will also reflect on other parameter combinations that are able to produce quasi-periodical dynamics. Although the model describes smaller populations, similar effects on a larger scale can offer a novel element for the explanation of periodical socio-economic phenomena, for example business-cycles.
3.4.3.1. The Basic Mechanism
Consider the picture below that shows a typical situation of oscillatory behavior generated by direct effects:
Plot of Avg . Boldness Plot of Avg . Boldness
0.7 0.6
0.6 0.5
0.5 0.4 0.4 0.3 0.3
0.2 0.2
10000 20000 30000 40000 50000 10000 20000 30000 40000 50000
Plot of Avg . Watchfulness Plot of Avg . Watchfulness 1
0.8
0.8
0.6 0.6
0.4 0.4
0.2 0.2
10000 20000 30000 40000 50000 10000 20000 30000 40000 50000 Figure 26 – Oscillatory behavior by direct effects with two different frequencies. Above are ABs and below the corresponding AWs.
- 130 - What happens here is closely related to norm cascades and their representation in the model. With a low W B is driven up, (here by the drift) and when it gets high enough so that the ignition level and the increasingly fluctuating Ws get close enough to each other, W shoots up by WUDP and pushes B down. This however, in turn, causes W to collapse because there is not enough punishment to support it. I call this kind of dynamics type I oscillation, when W displays short pulses, increasing suddenly but collapsing to its bottom level after pushing B down. From this bottom level determined externally (by WMIN) it can only take off when B reaches a considerable level again. As W always shrinks to the same level the level that B must reach before W could take off again is approximately the same each time. Adding that B is dragged up steadily, we can see why the amplitude and frequency of the oscillation appears to be stationary. What factors does determine this amplitude and frequency? There are many of them. Firstly all those that can influence the ignition level and the time it takes for W to reach it. But more important in this case is the rate by which B is dragged up (here BUNM) while W is low, as it is easy to see on the right hand side of the above figure, since until B reaches the level necessary to ignite floor level W, W cannot take off (in a reasonable time). For a similar token the speed by which B is driven down386 is also important. The picture below shows how this frequency changes by moving BUNM and BUDP.387
Periods Average Periods Between Local Maxima as BUDP and BUNM is Multiplied by a Factor
14000
12000
10000
8000
Factor 0.2 0.4 0.6 0.8
Figure 27 – Frequency of oscillation as measured by the average number of periods between neighboring local maxima in AB as we multiply both BUNM and BUDP with the same factor marked on the horizontal axis
The average number of periods between local maxima decreases as we increase the multiplying factor for BUNM and BUDP that is the frequency of oscillation increases. This, however, is not the only circumstance that influences the characteristics of the oscillation. We can see on Figure 26 that W practically immediately collapses after B went down. If, however, the floor level of B is close to the value that is able to support W’s high level, W will not be able to collapse for a considerable time, significantly extending the period of oscillation with a completely new phase inserted that was missing from the above examples: B cannot start increasing while W is still high. The left part of the picture below reveals this situation. (Observe how long periods of high and low adherence to the punishment norm alternate.388)
386 Approximately B*W*SR*BUDP−BUNM. 387 Note that for oscillation to appear the values of BUNM and BUDP must be tied together to some degree; otherwise a low BUDP could not counterweight BUNM even at a high W level. 388 The period of this oscillation is still rather regular. Should we use a different updating method for B, e.g. a noise without a drift we should find more irregular patterns.
- 131 -
Plot of Avg . Boldness Plot of Avg . Boldness
0.5 0.9
0.85 0.4
0.8 0.3
0.75 0.2
20000 40000 60000 80000 100000
10000 20000 30000 40000 50000 0.65
Plot of Avg . Watchfulness Plot of Avg . Watchfulness 1
0.8 0.2
0.6 0.15
0.4
20000 40000 60000 80000 100000 0.2
0.05 10000 20000 30000 40000 50000 Figure 28 – AB with a floor level close to the value that is able to support a high W (left), and W capped at break-even level of B (WMAX=0.25), preventing oscillation (right)
On the right part of the figure we can see an equally interesting situation. Capping W at the break-even level of B prevents oscillation and at the same time locks AB at an equilibrium level.389 This is even more interesting if we consider that B was governed in this case by BUR using discrete contribution, where the optimal level for B is always either 0 or 1, which is why we do not expect it to stabilize at values in-between. This stabilizing property of joint norm dynamics is probably the most important bit of the oscillatory topic: even when behavior is governed by a mechanism that always has a corner target, norm adherence can be relatively stable around internal values. Although the above situation seems to be a rather special one, we will see a more loose kind of stabilization as we let WMAX grow, and have the B and W levels oscillating around internal (break-even) values with a lower amplitude than above and in a continuous fashion (Type II oscillation). It will suggest us another important idea, too: the level of B that is able to support a given level of W. To understand this situation a bit more, it is useful to familiarize ourselves with a couple of necessary conditions for oscillation.
3.4.3.2. Conditions of Oscillation
These conditions are provided here for the special case we have been dealing with in this chapter: where B is driven by the drift upwards (BUNM>0) and the direct peer punishment downwards (BUDP<0), while W is carried by the direct peer effect upwards
389 There are at least two sources of this limited W. Firstly, it can come from limited resources of agents (time, attention, energy) that must be split among the neighbors resulting in imperfect surveillance of behavior. Secondly, external conditions can hinder punishment either at the stage of observance (low transparency of behavior), or punishing (no effective channels to deliver the punishment through).
- 132 - (WUDP>0) and the drift downwards (WUNM0=WUNM1<0). Nevertheless, to their analogy, it is possible to derive such conditions when other effects are involved. To achieve oscillation, first we need to make sure that punishment is severe enough so that with a high W (=1), B can be driven down. It is expressed by the following inequality:
−>BUDP* SR BUNM (3.20)
Next, we have to have a high enough peer effect on W so that W can move upwards when B is high (=1): 390
WUDP* SR2 >− WUNM (3.21)
Extending equation (3.21) we have a necessary condition that is needed for W to collapse at the floor level of B:
2 W** BF SR * WUDP<− WUNM (3.22)
From the last inequality we can obtain a necessary condition for the floor level of B for oscillation:
WUNM 11 BB<− = (3.23) F WUDP SR2 W W_ Break− even
This is the key condition for the oscillation dynamics of direct effects.391 On the one hand the inequality gives us the necessary condition mentioned above with the cap level AW substituted into W hat (1 or WMAX), and on the other hand substituting an actual AW level for it, we have the B level at which the expected change in W hat is zero: the break-even level B for a given W.392 (Above this level W will grow and below shrink on average.) Note that this level does not depend on the updating method for B. It is also important that this level is different (lower) than the one that is able to support a given level of AW as it will be explained shortly. In a similar fashion, starting from equation (3.20) and including B and W into its left hand side as in equation (3.22) we can obtain the level at which B would stabilize with a given W level (without the feedback in W).
390 Or the same with SR(SR−1) when CB_WUDS=0, as explained in footnote 384. The same goes to all equations here that include SR2. 391 Compare this with the formula for the ignition level of W. Not surprisingly it is the same without central punishment involved. 392 Once again, strictly speaking these conditions are true for individual Bs and the average W in each particular agent’s punishing neighborhood, but since oscillating populations mostly move together tightly, these equations are approximately true for population-wide averages also.
- 133 - BUNM 11 B =− (3.24) Stable BUDP SR W
To let W collapse we have to have this value be lower than the B level that is able to support cap W level.
3.4.3.3. The Supportive Boldness Level
To understand why the B that is able to support a given W level differs from the break-even level, let us return to Figure 28. As I have mentioned, WMAX was set at the break-even point for B. Due to the positive feedback in W we can be sure that with a high enough B W will be maxed out (at 0.25 in this case) if it is able to ignite at all. We can see that at this point B starts to fall because the simulation is written so that at the break-even level the optimum is already 0. (We use BUR instead of BUDP here.) As, however B approaches the level that can still support a W level of 0.25 it stabilizes, because when B goes below this level W begins to drop, too, which immediately switches the optimum to 1, raising B, and W also in turn. Therefore, we would expect that B stabilize near the level given by equation (3.23)393, which is about 0.375 (considering W being approximately 0.25, SR=2, WUNM0=WUNM1=−0.009 and WUDP=0.024). However, what we find is that B stabilizes at nearly 0.75. What causes this discrepancy? The answer lies partly in the positive feedback built into the direct effect, and partly in the stochastic nature of the model. At any given B level if W begins to decrease for any reason, even because of pure chance, it will make further drops in W more likely since peer punishment becomes less frequent. This is why at the break even level B although the expected change in W is 0, if by chance it decreases it would decrease further with an increased probability, in other words this equilibrium is an unstable one, thus the break-even level B would not be able to support the corresponding W for a long time. This is also the reason why B stabilizes at a significantly higher value, which is high enough to squeeze W strongly enough to the ceiling value so that this downwards positive feedback can be overcome. At what values will B stabilize in such cases? It would be hard to seek a better answer analytically than given by the above equations, but simulation can solve the problem again. The figure below compares analytical break-even levels given by equation (3.23) and simulation results for B levels that are able to support certain W values. (That is the stabilization level in the above situation.)
393 We cannot use equation (3.24), as B in this case is driven by BUR, not BUNM, and also because the reason for B’s stability here is not a fixed W, but that W reacts to B’s crossing a given value, which at the same time sends B to the other direction. Thus, the question here is that what B level supports a given W level, not what B level is determined by a given W.
- 134 - B Level B LevelB Level Where W Levels have an Expected Displacement 0 B Level Required to Support Different W Levels
SR =2 SR =2 0.8 0.8 SR =3 SR =3 0.6 0.6 SR =4 SR =4 0.4 0.4 SR =5 SR =5
0.2 SR =6 0.2 SR =6
W Level W Level 0.2 0.3 0.4 0.5 0.2 0.3 0.4 0.5
Figure 29 – Theoretical break-even levels for B (left) and simulated (right) B levels that are able to support different W levels indicated on the horizontal axis for different SRs with WUNM=−0.009 and WUDP=0.024
What we can see here is first that higher W levels require lower B (because of the positive feedback of WUDP). Another spectacular feature is that simulated values are usually higher than theoretical ones for the reasons described in the preceding paragraphs. One more thing to note is that with higher SRs theoretical and simulated values are closer to each other which comes from the law of large numbers: with a larger neighborhood the average (number of) punishments will be closer to the expected value, thus chance events that can trigger the positive feedback and thus diverge simulation results from the theoretical values play a lesser role.
3.4.3.4. Continuous Oscillation
As I have already hinted, there is a second type of oscillation that direct effects are able to generate. For this type the W level does not drop to its floor before it begins to rise again. This case generally sets in when we cap W with WMAX<1 (that is we suppose that agents are unable to check all of their neighbors in each turn with a high probability), but at a higher value than the break-even level of B. In such cases the typical picture we get is what you can see below.
Plot of Avg . Boldness Plot of Avg . Watchfulness 0.25 0.9
0.85 0.2
0.8
0.15 0.75
0.7 20000 40000 60000 80000 100000
0.65
0.05
20000 40000 60000 80000 100000
Figure 30 – Type II oscillation induced by direct effects, where AW does not hit the floor before it begins to grow again, resulting in more irregular dynamics. AB is on the left, whereas the corresponding AW on the right. (WMAX=0.26)
The intuition behind this kind of behavior is the following. As we let W be higher than the break-even level for B, B will not stabilize at the level that would keep W at its cap level
- 135 - since there the optimum for B is still 0. Thus B will go below it, consequently W begins to shrink until W reaches the break-even level for B, which turns B around. This time, however B has to reach a higher level than the break-even value for cap level W, since W is already smaller, which requires a higher B to keep it up. (As can be seen from equation (3.23)). Until B can reach this level, W shrinks on. This is what I call hysteresis in Figure 31. Since, however, we have capped W at a relatively low level that is still close to the break-even level of B, B will not be suppressed by a towering W to very low levels, which would require a substantial time to recover while W would drop to its floor level. Thus, in this case W is able to turn around while positive feedback still have a significant effect on it, requiring only a moderate B to assist. Thus, W to the contrary to the first type is fluctuating continuously as opposed to the pulses we observe with the first type. B at the same time for the same reasons will also have narrower amplitude. Moreover, as here we do not have the rather punctual synchronization provided by B needed to reach always the same level that is able to trigger floor level W, the fluctuations of both B and W are much more irregular than with the first type. What we can say about the level of this oscillation is that its range for W must include the break-even level for B, while the range of B must include the break-even level for the W for the break-even level for B (that is the break-even level for the value that must be inside the W range). Mark also for forthcoming considerations that the amplitude (and period) of the movement of both variables seems to be stationary. The following graph helps to grasp the gist of the joint norm dynamics.
- 136 -
Low W break-even level
B Hysteresis B break-even level W due to break-even level positive feedback in W High W break-even level
B break-even level
W
Extra stretching time of amplitude due to hysteresis
Figure 31 – Schematic illustration of the joint dynamics of B and W with type II oscillation generated by direct effects
3.4.3.5. Other Modes of Oscillations
As I have already mentioned direct effects are not the only mechanism in Contributron that is able to generate oscillatory phenomena. What we have to ensure is simply that B be affected by W (we have peer punishment), and W be also influenced by B in a way that high B drive W up, while low B let W shrink.394 How we move the B and W into the opposite direction can also vary, we do not have to stick to the drift. The following figures show cases for oscillation generated with different effects involved. First let us see a very similar picture to the type I case with direct effects.
3.4.3.5.1. Oscillations With Rational Updating
394 Technically, the opposite situation is also able to generate oscillation (low W brings B down, high B drives W down and low B makes W up). It is another question if it is possible to find a real-world analogue for such a setup.
- 137 - Plot of Avg . Boldness Plot of Avg . Boldness
0.8
0.8 0.7
0.6 0.6 0.5
0.4 0.4
0.3
20000 40000 60000 80000 100000 20000 40000 60000 80000 100000
Plot of Avg . Watchfulness Plot of Avg . Watchfulness 1
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
20000 40000 60000 80000 100000 20000 40000 60000 80000 100000 Figure 32 – Oscillation generated by BUR, BUDP and WUDP (left), and BUR, PPE and WUDP (right)
These pictures resemble to the ones that we have seen earlier because they still have the key element, WUDP, enabled, thus we still have the positive feedback in W. We can observe, though that the shape of the B peaks is quite different from what we have seen earlier, because B movement with BUR is not linear like with BUNM. Another difference is that when B is going down it falls not only because of BUDP, the direct effect, but also because (or simply because, when BUDP=0) the optimum of B, target value of BUR, switches over to 0.
3.4.3.5.2. Oscillations Without Direct Effects
The picture is different when we get rid of direct effects completely. Here is an example with fluctuating B and W levels, where oscillation is probably not the best word any more to describe the dynamics.
- 138 - Plot of Avg . Boldness Plot of Avg . Watchfulness
0.8 0.5
0.75 0.4
0.7 0.3
0.65 0.2
8000 16000 24000 32000 40000
8000 16000 24000 32000 40000
Figure 33 – Fluctuating AB and AW generated by BUR, PPE, WUNM0, WUND, PC and WUS with WUSC=0.1
In this case while B is moved by BUR and PPE like in the preceding case, the required dynamics in W was achieved by rewarding punishers with PC and applying a payoff-biased transmission for W. (With WUNM0<0 to let W decrease at low B levels). The noisiness of this picture comes from that we also had to set WUND>0, to keep a difference between individual Ws in order that biased transmission can move W according to their relative success.
3.4.3.5.3. Attenuated Oscillations
A remarkable and very clean picture is attained by simply setting WUNM0<0 and WUR>0, while driving B with BUR. Here is what we get.
Plot of Avg . Boldness Plot of Avg . Boldness 0.65
0.65
0.6 0.6
0.55 0.55
0.5
20000 40000 60000 80000 100000 0.45
0.45 20000 40000 60000 80000 100000
0.35
Plot of Avg . Watchfulness Plot of Avg . Watchfulness
0.8 0.7
0.6 0.6 0.5
0.4 0.4 0.3
0.2 0.2
20000 40000 60000 80000 100000 20000 40000 60000 80000 100000 Figure 34 – Attenuated oscillation generated by BUR, WUNM0<0 and WUR>0 (|WUNM|=|WUR|). The left part uses continuous, while the right part discrete contribution, otherwise all parameters are the same.
- 139 -
Although the original idea for WUR is that people are less willing to punish because they are sensitive to the price changes of punishment (more people to punish will increase their burden), it is possible to imagine circumstances for a positive WUR. For example people can be more aware of the need for being a punisher when they see defection in their proximity.395 While the main characteristics of this oscillation are similar to what we have seen in connection with direct-effects, there is an important difference. I have mentioned and also indicated on Figure 31 that direct effects introduce a kind of hysteresis into the joint dynamics of B and W due to the positive feedback in W which moves break-even levels in B for W according to equation (3.23). This is what is missing from the latter kind of attenuated oscillation, and this is the cause for that direct effects are able to avoid attenuation by stretching the amplitude. (In Figure 33 it was the noise that had a similar effect.) Now we can see the special relationship between direct effects and oscillations. Naturally, what I could include here is only a small fraction of what could be told about direct effects, norm cascades and oscillations among different parameter combinations. I have tried to concentrate on the most important general characteristics of these phenomena and pick some interesting cases that might demonstrate the potentials of the model. Before summarizing the chapter let me give one more example of oscillatory dynamics just to illustrate the variety of phenomena still waiting for exploration.
Plot of Avg . Boldness Plot of Avg . Watchfulness
0.9 0.5
0.85 0.4
0.8 0.3
0.2 0.75
4000 8000 12000 16000 20000 4000 8000 12000 16000 20000
Figure 35 – Attenuated oscillation with BUR, WUNM0<0 and WUR>0 (|WUNM| ≠ |WUR|)
3.4.4. Summary of Findings
In this chapter we have investigated the most important features of direct effects in Contributron, with two related phenomena: norm-cascades and oscillation. The most important findings are as follows:
● When norms are governed exclusively by direct effects, whereby the expected change in the measure of norm adherence is a linear function of its level and
395 Recall for example the works of Kosfeld and Huck, where higher criminality helped to keep up anti-defection activity.
- 140 - the probability of punishment is fixed, norm adherence has a characteristic half-life.
● When norms are jointly governed by a direct and another effect dragging it into the opposite directions, norm adherence has an equilibrium point.
● Norms affected by a positive feedback mechanism display cascades. More specially, willingness to punish driven by a direct effect has a typical threshold value (ignition level) depending on the current level of defection and other circumstances. In order that we can observe a norm cascade, this threshold value needs to be attained by only a sub-group, which in turn is able to drag the population with itself.
● In a system incorporating stochastic elements, the ignition level can be attained even without a sufficiently high level of defection due to chance events. Chance events are various, including imperfect replication and uneven distribution of defection and punishment.
● How easily a punishment norm can proliferate depends on several factors. In addition to the level of defection they include the magnitude of direct effects, the drift and the noise in updating, the (natural) floor level of punishment and the strength of the moral function of law.
● A seemingly stable state of cooperation may break-down abruptly due to stochastic events. Supposing that defectors are less willing to punish than cooperators, if a few agents’ willingness to punish reaches a critically low value defection can quickly spread throughout the population.
● Defection and willingness to punish can engage in a joint oscillatory dynamics, but it requires a number of necessary conditions to be satisfied. The frequency of these oscillations depends primarily on the speed of growth in defection when willingness to punish is low and the speed of decreasing when willingness to punish is high.
● There are at least two types of oscillation related to direct effects. The first type implies short outbursts of peer punishment, while the second a continuous floating around break-even levels.
● Due to stochastic elements, the break-even level of defection for willingness to punish is different (lower) than the level that is able to support the same punishment level on the long run. Break even levels are within the range of oscillation, while the supporting level is the point of stabilization of defection when willingness is capped at the break-even level.
● Oscillations can be observed with several means of updating. The characteristics of oscillations depend largely on our actual assumptions on agent behavior.
● Oscillatory dynamics generated by direct effects have a characteristic hysteresis that prevents attenuation of amplitude. While noise is also able to
- 141 - keep norm adherence moving up and down, other types of updating often result in attenuation and stabilization of defection and punishment behavior on the long run at the internal break-even levels.
Naturally, in real social life processes are never so clear-cut as in a model.396 People have memory, so they can remember that when their morals plunged they got punished and avoid defection next time; members in groups migrate, interfering with the ongoing processes; and external effects influence what is happening inside. Nevertheless, as we have seen in the first part, norms are variable phenomena and they also can influence each other. What the model suggests is that in certain circumstances with certain well-defined assumption this interrelatedness can result in interesting co-evolution patterns, and even if the real picture is more complex, it helps us to grasp some of the links and forces in action between them. At the same time, there is nothing to prevent further extensions of the model, incorporating mechanisms that may interfere with the dynamics described in this chapter, which will allow for an even more accurate approximation of real-life socio-economic behavior.
3.5. Heterogeneous Populations, Network Variations
Turning from model components to applications the first topic we examine is how ©ontributron can be used to explore the properties of heterogeneous populations and the consequences of different network arrangements. One of the main advantages of Contributron is that all parameters and initial conditions can be customized for each individual agent, enabling the experimenter to compose heterogeneous populations, just like it is in real societies. It must be emphasized that Mathematica is able to manipulate standard text files, and this way modifying the ini file can also be controlled and programmed from within Mathematica. This way, complex experiments can be set up and let run for a long time collecting data automatically requiring no human supervision. To facilitate modeling of stratified populations the experimenter can define not only individual agents but agent types simply by telling the program how many instances of a special agent to create. Although these agent groups are created in blocks they can be mixed together to any desired extent by specifying a shuffle method. The primary aim of this chapter is to demonstrate how to use Contributron in modeling heterogeneous populations. But heterogeneity does not only mean agent heterogeneity. It can also be network heterogeneity, covering all the possible ways agents can be connected in a social network. The secondary aim of this chapter is to show how network structure interferes with outcomes. In the previous chapters at different points I have already dealt with different network setups, but it will be instructive to pay closer attention to this issue. It is also apt to be presented in conjunction with heterogeneous populations, as network heterogeneity can easily interfere with agent heterogeneity, resulting in different outcomes with different agent type compositions. My primary aim here is to give ideas and examples on how to simulate and analyze heterogeneous populations using the model and along the way derive some basic results. The
396 It should also be considered that in this chapter we have only used a small fraction of what is already available in the model, right because it made it possible to explore the basic underlying mechanism of these fundamental phenomena of joint dynamics.
- 142 - didactic objective is the reason for resorting to simple setups. 397 At the same time, this approach allows for identifying some of the most important mechanisms related to our present agenda greatly affecting output, which otherwise could be much harder to dig up. Heterogeneous agents in heterogeneous networks can influence each other in very subtle ways, and in complex simulations these effects all appear superimposed and deeply entangled. What I can achieve here is to identify and emphasize some of the most general and most impetuous interrelations by setting up simple and transparent experiments. All-in-all, I do not intend to put forward that these are the most realistic combinations the model is capable of. (I hope they are not.) In this chapter first we are going to mix different fractions of maximizers with other types: to begin with we put them into a population of average-biased imitators, then payoff- biased imitators and we are going to compare the two cases. Next we examine how changing SR that is the number of neighbors affects the results obtained until that point. Following an interlude with an interesting example on network effects, we move to punishers. First we couple them with maximizers, then payoff-biased imitators and agents being affected by direct effects. In turn we allow for variable Watchfulness levels, a scenario that seems very complicated at first sight but which brings surprisingly similar results to the simpler cases. Next we will mix average and payoff-biased imitators and see how populations with different proportions behave. All along the way we allow for different network configurations to be compared for the different populations. Finally we introduce a tool to generate isolated sub- networks that will be applied in the chapter on experimental connections.
3.5.1. Maximizers
For Economics it has been an important question if people can be seen as maximizers universally. Let us start on this pathway and investigate an exciting question: what happens if only a fraction of people are capable to recognize and follow the right strategy directly, while the rest free rides on them by copying their strategy either by picking the best or just adapting to an average of their neighborhood.
3.5.1.1. Maximizers and Average-Biased Imitators
The following diagram shows how a growing fraction of maximizers put into a population of average-biased imitators changes the speed of convergence to the optimum and its standard deviation on different networks.
397 This means for example that to demonstrate network heterogeneity I am going to use the built-in network types. These simple arrangements are used in the literature right because of their transparent structure, which is why it is useful to be aware their properties and compare how they influence the output.
- 143 - Periods Periods Needed to Reach Optimum RCOR StandardStd . Dev Deviation . of Periods Needed to Reach OptimumRCOR 8000 8000 RCHP 7000 RCHP 6000 6000 RCHR RCHR 5000 4000 4000 RING RING 3000
2000 LINE 2000 LINE 1000 % of Maximizers % of Maximizers 4 6 8 10 12 14 4 6 8 10 12 14
Figure 36 – Periods needed to reach 95% of the optimum of 0.833 (E=TR=1, CPR=0.2, CPE=−3) from a default initialization of B and W with different fractions of maximizers and average-biased imitators on different networks (left) and its standard deviation (right). (SR=2, BUR=0.1 for maximizers and BUS=0.1, BUSC=1 for imitators)
What is important here is not the actual values, as they depend on the actual settings, but the general pattern. Also note that in a connected network (where there are no isolated sub-groups) sooner or later all agents would converge even if there is only one maximizer and the rest of the population consists of any kind of imitators. This is the reason why the above picture informs us about the speed and not the wellness of convergence. What might stand out at first sight is that out of the built-in network types the RCOP one is not included. It is so because it often does not reach the optimum at all especially with a low SR, because of the possible isolation of agents and sub-groups already explained. Secondly, we can see that as we approach low percentages of maximizers the number of periods to convergence rises (which is quite natural), and it does so at an increasing rate for all network types. Next we can see that it took the longest for LINE to converge, closely followed by the RING network, which seems quite logical again: information spreads slowly as agents are connected always to the same neighbors without small-world connections.398 (Notice the low SR used.) Observe further that although the RCOR network is also fixed it converges much faster than the LINE or the RING due to its randomness which generates small-world connections and lowers average distance. (Compare it with our findings in the first chapter.) It is mostly close to the changing networks, and it is only worse than them at low percentage of maximizers, where we can see that for this network the standard deviation of the number of periods needed to reach that value raises suddenly. It happens so because with a low number of maximizers it becomes increasingly important where those few maximizers are located on the actual network, and how the network is wired: if maximizers have a good position that is linked richly to imitators, we see a faster convergence.399 (An example of interplay between agent and network heterogeneity.) Another thing to notice is that the RCHP and RCHR networks has a very low variance of convergence that is they always converge in about the same number of periods. This is caused by their continuously changing nature: convergence does not depend on an invariable initial choice, and the position of maximizers on it like in the case of all fixed types400. One
398 Note that on LINE and RING networks I have used the randomize type of shuffling to scatter the maximizers throughout the population. On random networks it was not necessary as links do not depend upon the serial number of agents. 399 A higher number of maximizers makes it more probable that they are distributed “more evenly” that is there is a lower probability that they remain in isolation. 400 RCOP, RCOR, LINE and RING
- 144 - more notable feature is that the RCHP network is still slightly worse than the RCHR: on a probabilistic network not only the position of normal connections change, so does their number, which brings in an extra source of uncertainty into the dynamics. There can be isolated agents / groups in each turn which does not last long, but can hinder convergence. One important aspect of the above figure on convergence time is that we can tell not only that how much slower or faster convergence is on the different network types but it also enables us to state how much more or less maximizers are necessary in different circumstances to achieve that same speed. Many of the graphs below have a similar use. There are at least two departures from the above situation that are worth a look. First, it would be interesting to see what happens if the rest of the population consisted of payoff- biased imitators instead of average-biased ones. Second, one might like to know how a higher level of connectedness affects convergence on the particular networks.
3.5.1.2. Maximizers and Payoff-Biased Imitators
We start with the former, and consider the figure below depicting the same statistics as above for maximizers mixed up with payoff-biased imitators.
Periods Periods Needed to Reach Optimum Periods 8000 RCOR Standard Deviation of Periods Needed to Reach OptimumRCOR 12000 7000 RCHP RCHP 6000 10000 5000 RCHR 8000 RCHR 4000 RING 6000 RING 3000 4000 2000 LINE LINE 2000 1000 % of Maximizers % of Maximizers 4 6 8 10 12 14 4 6 8 10 12 14
Figure 37 - Periods needed to reach 95% of the optimum of 0.833 from a default initialization of B and W with different fractions of maximizers and payoff-biased imitators on different networks (left) and its standard deviation (right). (SR=2, and BUR=0.1 for maximizers and BUS=0.1, BUSC=0 for imitators.)
Intuition suggests that if agents do not blindly imitate an average strategy in their neighborhood, but they are able to pick the best, convergence to the optimal strategy should be faster. This should be even more true because Bs were initialized with a uniform distribution between 0 and 1, thus even certain non-maximizers are also close to the optimal strategy by default. This is why it is surprising to see that if anything, convergence becomes slower, especially at low percentages of maximizers and random networks. What can lie behind this phenomenon? Considering the right part of the above figure we can find the explanation. What we see is that the standard deviation of all random networks has strongly increased relative to the preceding case. Calling back the process of payoff-biased imitation we can understand why it is so. In this case as opposed to the average biased conditions, it becomes important how R of the particular agents evolve over time, which is strongly influenced by contingency through probabilistic defection and punishment, thus making convergence noisy, which particularly
- 145 - where it was fast in the average-biased case, entails an increase in convergence time. (As the number of periods needed to converge cannot be lower than zero.) Otherwise the general pattern remains the same: slowly converging LINE and RING and relatively quickly converging random networks.
3.5.1.3. Imitation and Sight Range
Let us next consider how raising the SR influences the output.
Periods Periods Needed to Reach Optimum Periods 2000 RCOR Standard Deviation of Periods Needed to Reach OptimumRCOR 2000 RCHP RCHP 1500 1500 RCHR RCHR
1000 1000 RING RING
500 LINE 500 LINE
% of Maximizers % of Maximizers 4 6 8 10 12 14 4 6 8 10 12 14
Figure 38 - Periods needed to reach 95% of the optimum of 0.833 from a default initialization of B and W with different fractions of the population maximizers and average-biased imitators on different networks (left) and its standard deviation (right). (SR=6, and BUR=0.1 for maximizers and BUS=0.1, BUSC=1 for imitators.)
(You should compare this picture with Figure 36. The only difference in parameters is that SR is 6 here instead of 2.) Just as one would expect, the number of periods needed for convergence decreased on all network types because information can spread faster. Accordingly, the really big drop in convergence time is observable in the case of RING and LINE where information spread most slowly, otherwise all general characteristics of the left hand graph are the same as on Figure 36. Getting a glimpse on the standard deviations we see that for those with a considerable variability in the baseline case (RCOR, RING, LINE) all decreased. This is not surprising: giving more connections to agents implies not only that information spreads faster, but also that convergence depends less upon where the maximizers are located: the probability of isolation is lower, there are more alternative routes and the average distance between agents decreases.401
3.5.1.4. Detour: Perils of Network Effects
Running the experiment with different SR values at this point indicated that there is something special going on in the LINE and RING network types that might be in connection with their structural arrangement. It is instructive to examine this issue, because it highlights the subtle ways connection layout can interfere with convergence. Consider the following figure depicting the evolution of AB with different SRs on RING.
401 It is also noteworthy that by increasing SR network types become more similar to each other for they are all converge towards the FULL type.
- 146 -
0.8 0.8
0.75 SR =1 0.75 SR =2 SR =3 SR =4 0.7 0.7 SR =5 SR =6 0.65 0.65 SR =7 SR =8 0.6 SR =9 0.6 SR =10 SR =11 SR =12 0.55 0.55
100 200 300 400 500 100 200 300 400 500
Figure 39 - AB (averaged over 5 runs) on a RING network with average-biased imitators and one maximizer for odd (left) and even (right) SRs
What we find is that the path of AB evolves totally differently as we increase SR through odd or even numbers. If we only pick odd numbers for SR, convergence becomes gradually worse, while with even numbers it improves. Nevertheless, the limit seems to be common. We have a similar pattern if we use LINE instead with the same parameters, but if we switch to payoff-biased imitators (on RING) the following picture is obtained.
0.86 0.85 0.84 0.825 SR =1 SR =2
0.8 SR =3 0.82 SR =4 SR =5 SR =6 0.775 SR =7 100 200 300 400 500 SR =8 0.75 0.78 SR =9 SR =10 0.725 SR =11 0.76 SR =12
100 200 300 400 500 0.74
Figure 40 - AB (averaged over 5 runs) on a RING network with payoff-biased imitators and one maximizer for odd (left) and even (right) SR
There is no quality difference between the two sides: convergence seems to get gradually better with SR. (Observe also the noisiness of the pictures. It shows what already been mentioned: payoff-biased imitation brings in extra sources of randomness into the dynamics.) Thus, the curiosity of Figure 39 must be connected to average-biased imitation. We must extend our investigation to agent level to find an explanation for this strange phenomenon. On the one hand it is not difficult to see why payoff-biased imitation results in a better convergence with an increasing SR: all agents see more neighbors, thus they can choose the best strategy from a larger assortment and they can also transmit it to more agents. On the other hand, with average-biased agents the picture is not that clear. Firstly, convergence can get better, for the same reason: information can be transmitted through a greater distance. Secondly, however, average-biased agents cannot pick the best the strategy: if they already could copy the best (or a good) strategy, raising SR only makes their convergence worse because the weight of the good strategy is decreased. This is particularly important when there are few maximizers. Increasing SR, the neighbors of the maximizers will only see worse agents, so they will transmit to their neighbors worse strategies, not only themselves having an inferior convergence, but at the same time obstructing the further spreading of the optimal strategy. Even on changing networks, when an agent is connected to the maximizer it will
- 147 - have a lower weight with a higher SR, but then, all agents has an equal chance to copy the best (and all other) strategies, thus all imitating agents in the population will be constantly close to a common B level, so the opportunity to copy the best is optimally exploited, close neighbors to the maximizer cannot isolate him.402 On a fixed network, even more on LINE and RING, where average distance is high, certain agents can only attain the best strategy by sequentially copying and transmitting it, thus agents far from the maximizer in distance will be relatively far also in strategy and AB will not improve as much per turn as it could given that they also have a chance to a more direct connection. With average-biased agents the actual change we see in convergence by increasing SR is affected by both of these meliorating and deteriorating effects.403 This, however, does not tell us why convergence with odd and even SRs differs so markedly. To find an explanation, first recall that on a RING or LINE network with odd SR, all agents see one more neighbor on the same side. Next consider that with SR=1 on a RING all agents copy only one (and usually a better) strategy than what he has as the copied agent is closer to the maximizer on the chain, thus the best strategy is transmitted without obstruction to all agents through a direct route. Raising SR, though we open another route on the other side of the maximizer, it is overwhelmed by that now agents will begin to copy strategies farther from the maximizer than themselves, thus we are able to imagine that convergence deteriorates. Besides with odd SRs there is a directional preference remaining in the information transmission (due to the asymmetrical connections) which amidst the interplay of the effects described in the last paragraph seems to speed up convergence. This difference between odd and even SRs gets weaker as SR grows, since the fraction of number of connections on the two sides goes to one, which is why consecutive odd and even AB trajectories get gradually closer to each other. Finally, it is instructive to see how SR affects convergence on an unstructured (changing) network (RCHR).
402 Note that when an agent with a B far from the optimal strategy is connected directly to a maximizer his B (and AB) improves more than when someone else has the opportunity, who is already close to the best strategy in terms of B. 403 The complexity of the interplay between these effects manifests in that the convergence were not always completely orderly even among the odd and even cases: populations with lower SRs were sometimes closer to the limiting case than others with a higher one. The most striking pattern, however, is the odd-even discrepancy.
- 148 - 100 200 300 400 500
0.9 SR =1 SR =2 SR =3 SR =4 0.8 SR =5 SR =6 SR =7 0.7 SR =8 SR =9 SR =10 0.6 SR =11
0.5
Figure 41 – Convergence of AB on a RCHR network with one maximizer and a population of average-biased imitators.
What we see here is a completely smooth transition: higher SRs always resulting in faster convergence. For convenience, here is the intersection of the above data points at period 100 in order from SR=1 to SR=11:
{0.711, 0.748, 0.762, 0.766, 0.772, 0.774, 0.777, 0.778, 0.779, 0.781, 0.781}
Although in real social groups such abstract networks as RING and LINE are not very likely to be found, they are used in simulations for their simplicity. This example on the one hand calls attention to the importance of involving enduring social networks into our analyses as opposed to random pairing because structural effects can and do essentially change the nature of dynamics. On the other hand it also shows how seemingly little changes in social network structure can fundamentally affect the results, and it emphasizes the possible artifacts that network modeling without due analysis can inadvertently build into results.
3.5.2. Punishers
As indicated in the first part, people are different with respect to how much they are willing to punish free-riders. This has been recognized by Experimental Economics, and several evolutionary models have been built on this idea. This is why it is an exciting question to see what happens in Contributron when we set it up to model populations where heterogeneity is based on mixing punishers with agents differently updating their Bs: maximizers, imitators and agents sensitive to direct effects.
3.5.2.1. Punishers and Maximizers
- 149 - First we consider how MAB moves by mixing different percentages of punishers into a population of maximizers.
MeanMean Avg . Average Boldness Boldness with Different % Punishers RCOP MeanMean Avg . Average Boldness Boldness with Different % Punishers RCOP 1 1 RCOR RCOR 0.8 0.8 RCHP RCHP
0.6 RCHR 0.6 RCHR
0.4 RING 0.4 RING
LINE LINE 0.2 0.2
% Punishers % Punishers 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100
Figure 42 – MAB with different percentage of punishers in a population of maximizers on different networks (W=0.5 for punishers, BUR=1, SR=2, PPE=−5, E=TR=RA=1). (All agents maximize, but only a fraction punishes.) Asymmetric (left) and symmetric networks (right).
Notice that here I am using MAB again instead of the periods needed for convergence because here it is not guaranteed any more that the population and all of its members will converge to the same optimum after a time. The first thing we see is that on all networks MAB decreases with the percentage of punishers, which is quite intuitive. The second thing we see is that there are basically two distinct regimes: one with slower convergence, and another below. We can see that on both symmetric and asymmetric networks the lower arm includes the LINE and RING, while the upper arm the RCHP and RCOP networks. (I have already explained how a greater variance in the number of punishers (indirect connections) can result in less effective punishment under Figure 8, which is happening here.) At the same time RCHR and RCOR switch position from the upper to the lower as we move from asymmetric to symmetric networks. This is again a manifestation of the change in the distribution of number of punishers: for regular networks it is always SR in the symmetric case (like on RING), and it has the familiar binomial distribution in the asymmetric case (that is the same as for probabilistic networks). We can also notice that the LINE does a bit worse than RING, which comes from that there are less connections. To be able to deliver the symmetric case the above simulations were executed with only a population of 20, and this is why the difference between these two networks is perceptible. I have also run the simulation with the above parameters but with a population of 100, where as expected the difference between them has disappeared. Otherwise all general characteristics have been the same, thus the above figure can be compared to the simulations below using a population of 100 by default. Just as before, these graphs report not only how much weaker punishment is with a given percentage of punishers on different networks, but they also tell us how much more punishers would be needed to compensate in MAB levels for the different network structure.
3.5.2.2. Punishers and Payoff-Biased Imitators
Let us now see how MAB moves if we put our punishers into a population of payoff- biased imitators instead of maximizers.
- 150 -
Std . Dev . of MAB MeanMean Avg Average . Boldness Boldness with Different % Punishers RCOP andard Deviation of Mean Avg . Boldness with Different % PunishersRCOP 1 RCOR 0.06 RCOR 0.8 RCHP 0.05 RCHP
0.6 RCHR 0.04 RCHR
0.4 RING 0.03 RING 0.02 0.2 LINE LINE 0.01
% Punishers % Punishers 20 40 60 80 100 20 40 60 80 100
Figure 43 - MAB (left) with different percentage of punishers in a population of payoff-biased imitators on different networks (W=0.5 for punishers, BUS=0.1, BUSC=0, SR=2, PPE=−5, E=TR=RA=1), and its standard deviation (right).
With imitation, network structure influences not only that how many punishers the agents have, but it also plays an important role in the selection of strategies (which is done individually by BUR or the direct effect). Thus it is understandable that these simulations were generally noisier than those with maximizers, which made it necessary to run the simulations longer for better convergence. I have also used a larger population to be able to better capture this information spreading and also to have more data points for averaging. These, however, greatly slow down symmetric network generation and in turn simulation on changing networks, thus instead of the symmetric case the standard deviation of MAB is displayed on the right, which is also instructive. There are quite a few differences from the maximizer case and other peculiarities on the above pictures. What is common is that LINE and RING are again close to each other, also because of the larger population. The first important difference is that punishment became most effective on changing networks, which is again connected to better information spreading. On a fixed network when an agent is punished, his neighbors will see that it is not worth to shirk; therefore their Bs will go down. This process, however, stops here because the neighbors if they are not punished themselves will do worse with a lower B, therefore low B will not spread further. On a changing network every agent has an equal chance to see punished agents (including the punished himself), and the ability to select from a variety of strategies will make the overall effectivity of punishment higher. (On a fixed network after a time exactly those agents with a higher B (capable of faster convergence) will be isolated from seeing examples of punishment.) We can also see that RCOP starts lower than the other networks: it does not reach MAB=1 even without punishers. It is caused by isolated agents, who do not see anybody else, thus they cannot compare strategies. On the other hand it ends up higher than the others for the same reason, therefore it can be said that it is less sensitive to changes in the percentage of punishers. Moreover, we find that the RCOR moves more or less parallel with RING and LINE, but there seems to be a systematic discrepancy, as shown on the following figure.
- 151 - MeanDifference Avg . Boldness between Mean Average Boldness with RCOR and LINE
0.06
0.04
0.02
% Punishers 20 40 60 80 100 -0.02
Figure 44 – Difference between MAB of RCOR and LINE on Figure 43
This picture tells us that punishment is less effective on RCOR than on LINE (and RING) either when there are too many or too few punishers in the network, but more effective between the extremes. Although the number of normal contacts is the same on the two networks, the number of inverse contacts has a binomial distribution on RCOR as demonstrated above. This, especially with many punishers, when B is low, results in less effective punishment as also has been shown already. On the other hand, it is also true that those punished can be observed by a variable number of agents. Considering that these agents are punished by someone, they are watched by at least one agent, the punisher (and the more punishes an agent, the more will watch them in the same fashion.) This is why the punished agents will have a higher than average number of inverse contacts, in other words the more an agent is punished, the more will see that his strategy is bad, therefore low B will spread faster, therefore punishment will be more effective. The above picture results from the interplay of these effects. Take a look at the standard deviation of MAB on the different networks on Figure 43. What we find is that it is generally higher in the middle than at the edges. The explanation is that when the population is heterogeneous, network structure (and arrangement of agents) will not only determine how many contacts an agent has, but also what kind of agents he will be contacted to, thus it will have a stronger effect on the outcome, therefore we will see greater variability between different seed runs. Not surprisingly this hump shape is more articulated for fixed than changing network types, since the outcome in fixed networks is more dependent on the one and only network arrangement than in changing networks on the ephemeral changes of the constantly shifting structure.
3.5.2.3. Punishers and the Direct Effect
To complete the examination of the effectivity of peer punishment with differently updating agents now we put our punishers into a population sensitive to the direct effect.
- 152 - MeanMean Avg . Average Boldness Boldness with Different % Punishers RCOP 1 RCOR 0.8 RCHP
0.6 RCHR
0.4 RING
LINE 0.2
% Punishers 20 40 60 80 100
Figure 45 - MAB with different percentage of punishers in a population where B is updated by direct effect on different networks (W=0.5 for punishers, BUDP=−0.1, BUNM=0.015, SR=2, and E=TR=RA=1)
This figure shows the basic setup, where W is still fixed for punishers, like in all cases so far. While this picture is in many respects similar to the preceding case, there are also a couple of differences. First, here information spreading in terms of imitation is not an issue, making network structure (within the same type) less important and thus the output less noisy. We again find that the changing networks are generally better (punishment is more effective on them) than fixed ones. The explanation is also similar: punishers can be contacted to all agents, and thus they are able to punish their higher B peers. Meanwhile, we notice that at low punisher percentage the changing networks do worse for a while. This is caused by another phenomenon: when there are a small number of punishers, with respect to overall AB it is better to punish fewer agents. It is so because many of the agents will have B=1 (for BUNM raises it to the ceiling), and BUNM is only able to raise AB when there are some agents below this. If punishers are contacted to more agents in consecutive turns like with changing networks, BUNM will be able to take effect on more agents and therefore raise AB more than when punishers are connected to the same agents, like on fixed networks. With RCOR and RCOP we have the familiar phenomenon of binomially distributed inverse contacts, making punishment less effective.
3.5.2.4. Punishers with Variable Watchfulness
Let us further complicate the situation by one step. In the next experiment in addition to the direct effects working in B, W was also allowed to move for punishers. What is more, it was updated by WUDP, which has been demonstrated in the preceding chapter to be able to produce norm cascades and quite tricky joint dynamics. Just to illustrate the complexity of the situation, take a look at on how B and W move with a particular setting in this situation.
- 153 - Plot and Grid of Indv . Boldness 0 0 2000 4000 6000 800010000 2000 2000 0.8 4000 4000 0.6 0.4 6000 6000 0.2 8000 8000 10000 10000 020406081000 Plot and Grid of Indv . Watchfulness 0 0 0.8 2000 2000 0.6 4000 4000 0.4 6000 6000 0.2 8000 8000 10000 10000 2000 4000 6000 800010000 020406081000
Figure 46 – Individual B and W moving wildly at a particular point of Figure 47
This is the situation when intuition does not help any more, we have to sit back and watch what is happening. Surprisingly, as we can see below, the outcome is in great part similar to the fixed W case in Figure 45.
Mean Avg . Boldness Mean Average Boldness with Different % Punishers RCOP MeanMean Avg Average . Watchfulness Watchfulness with Different % Punishers RCOP 1 RCOR 0.8 RCOR 0.8 RCHP 0.6 RCHP 0.6 RCHR RCHR 0.4 0.4 RING RING
LINE 0.2 LINE 0.2
% Punishers % Punishers 20 40 60 80 100 20 40 60 80 100
Figure 47 – MAB (left) and MAW (right) with different percentage of punishers with variable Ws for punishers updated by WUDP on different networks
All characteristic features are the same as with fixed W. The most visible change is that changing networks became even more effective. A possible explanation is that moving around punishment not only holds B down directly, but it also helps W to ignite. (Recall that higher B agents ignite easier.) Taking a look at the MAW, we see that changing networks achieve this low level of B with a moderate MAW, which is lower than that of either LINE or RING. (This lower W is used more effectively, though, by punishment applied to all agents with equal chance.) Another thing to notice is that not only B decreases but W also grows with the number of punishers: more punishers will generate much more punishment not only because there are more punishers, but also because their probability to punish is higher. It is caused by the positive feedback. More punishers (those who are allowed to have W>0) implies that it will become easier to become a punisher (for these agents to actually have a W>0).
- 154 -
3.5.3. A Mixture of Average and Payoff-Biased Imitators
Not only individual maximization, but being a payoff-biased imitator can also be more costly than simply copying an average, because the relative success of neighbors must be considered. This is why it is probable that free-riding can occur in this context as well, average-biased imitators relying on their payoff-biased peers. Let us finally consider what results we obtain by mixing average and payoff-biased imitators.
RCOP RCOP MeanMean Average Avg . Boldness Boldness with Different % Payoff Biased MeanMean Average Avg . Boldness Boldness with Different % Payoff Biased 1 1 RCOR RCOR
0.9 RCHP 0.9 RCHP
0.8 RCHR 0.8 RCHR
0.7 RING 0.7 RING
0.6 LINE 0.6 LINE
% Pyf . Biased % Pyf . Biased 20 40 60 80 100 20 40 60 80 100
Figure 48 – MAB of populations consisting of different rations of average and payoff-biased imitators on different networks with CPR=0.2, CPE=−3, BUS=0.1, E=TR=1, (Optimal B=0.833). SR=2 (left) and SR=10 (right)
Basing on the insights already acquired, it is not difficult to explain the general features we find here. First, naturally, as we raise the percentage of payoff-biased agents, the MAB gets closer to the optimum. Second, with a low SR RCOP converges least, again because there are agents who are not connected to the population. Third, LINE and RING converge also quite slowly, because of the high distance the information must travel. Fourth, changing networks converge better than constant ones because of their better information mixing (agents farther from the optimum can access it.). Fifth, RCHP converges best, most probably because payoff-biased imitators can compare more strategies when they have an above average number of contacts, which seems to help overall convergence more than hinders it when they have less than average. (It also can be seen on Figure 43.) A higher SR slightly changes the situation. Interestingly, RCOP becomes one of the best converging networks. The reason is that there are no disconnected agents any more, and therefore that payoff-biased agents can compare more strategies to pick the best will dominate. Another notable difference is that constant networks seem to achieve better this time than changing ones. The probable reason is that on constant networks with high SR payoff-biased agents can swiftly transfer information by copying each other in a chain, while if we randomize the network in all periods, these chains are broken before more than one succession could take place.
3.5.4. Isolated Sub-Networks
Last in this chapter I would like to introduce an instrument which I have added to the model, and which can help better capture more realistic social networks. As hinted earlier,
- 155 - social networks are many times clustered. This additional feature makes Contributron capable to generate custom networks with (relatively) isolated but inside densely connected sub- networks, between which the level of connectedness can be controlled by the experimenter. A Mathematica function404 makes it possible to generate an arbitrary number of isolated sub- networks, within which the connection structure can be any of the built-in types. The function uses the executable to produce the sub-networks, which it loads into Mathematica and places them onto the main diagonal of a super-network. The resulting network can then be further manipulated in Mathematica, exported and loaded as a custom network through the ini file. The rate of connectedness between the sub-networks can than be controlled by choosing the NW_CUSTOM_RANDOMIZE network type instead of the standard NW_CUSTOM, and setting SR to the desired number of swaps of connections in the network.405 The following graph shows superimposed but completely isolated sub-networks in action. (The last chapter uses this feature for simulating real-world experimental setups.)
Plot and Grid of Indv . Boldness 0 0 0.8 2000 2000 0.6 4000 4000 0.4 6000 6000 0.2 8000 8000 2000 4000 6000 800010000 10000 10000 010203040 Figure 49 – Superimposed but isolated sub-groups, using the direct effect, BUR, average-biased and payoff-biased updating for B, respectively
3.5.5. Summary of Findings
The main findings of the chapter:
● When the majority of the population imitates a few maximizers the presence of small-world links can significantly speed-up information transmission and thus overall convergence.
● Payoff-biased transmission results in noisier dynamics of defection probability than average-biased, which especially where the average defection level has been low in the average-biased case entails an increase in overall defection.
● Norm dynamics in networked societies can be greatly influenced by the structure of connections. This emphasizes the importance of including social networks explicitly into our analyses, and calls for a careful choice of the network model with a thorough technical analysis of its underlying mechanisms to identify potential artifacts.
404 blockNetwork[…] 405 This method ensures that the overall connectedness of the network remains the same. Alternatively, the network can be modified from within Mathematica before exporting.
- 156 - ● Imitative transmission further increases the importance of network structure. Changing networks depend less on an initial choice therefore they have a relatively small variance of number of periods until convergence.
● Symmetry of random networks influences outcome by fixing number of punishers (inverse contacts) for all agents. When a random network is asymmetric this is a random variable having a binomial distribution, which often deteriorates effectivity of punishment, especially when otherwise defection is low.
● When punishers themselves also imitate in a population of imitators, overall effectivity of punishment is higher because punished agents are observed by above average number of agents on any random network type.
● The more heterogeneous a population is, the more noisy norm dynamics tend to become. The explanation is that with heterogeneous agents network structure and/or the arrangement of agents determine not only the topology of the network but also that how the different agent types are connected to each other.
● Increasing the share of punishers on a network of direct effect updated W does not only decreases B by the greater number of punishers but also through the increased level of punishment probability.
● A variable number of connections can also improve convergence through presenting more alternatives to payoff-biased imitators.
● On fixed networks payoff-biased agents with a high number of neighbors can transmit information about the best strategy swiftly around the network by copying it from each other in a chain. On changing networks these chains can not exist, which hinders convergence.
3.6. Policy Issues
One of the main objectives of practical Economics has been to help decision makers in choosing optimal policies in different economic situations. Analytical models have succeeded to advise policy makers in many circumstances, however, as usual these models were built on stringent assumptions partly made by the prevailing economic paradigm, partly by the particular models. Simulation offers a novel way to explore the consequences of various assumptions concerning both economic agents and their interactions in more complex and probably more realistic environments. Moreover, it enables the experimenter to vary policy parameters to find optimal strategies quickly in intricate situations hardly penetrable for analytical methods. Contributron is also able to deliver insights about how different assumptions described by the numerous parameters and settings available affect strategic statistics and how they result in different optimal policies. Because it is a good starting point and to ensure comparability with economic models in most of the forthcoming experiments I am going to use a population of maximizers. At the end of the chapter, however, I will add a short example which uses imitators, just to indicate that policy issues can be taken further towards agents with different behaviors, heterogeneous populations and various networks. I must again stress that what is covered herein is only a
- 157 - very special selection of topics that the model is capable to handle. The extent of this chapter, however, is only sufficient to demonstrate some basic setups and hint on potential departures. In this chapter we start off by defining our policy parameters and the performance measures we are interested in: the policy statistics. Next we will see how our first policy parameter, TR gives rise to an analogy of a real-life phenomenon: Laffer-curves. Then we turn to policy making with CPR and CPE that is certainty and severity of central punishment, and we will examine how they affect agents in increasingly complicated circumstances. We begin with the classical setup: maximizers and central punishment only. This will allow us to reproduce some predictions of Economics of Crime and also to compare our findings with analytical solutions. In turn we allow for peer penalty, first static then dynamic and will demonstrate how Contributron enables us to find optimal certainty levels in complicated situations. Here we will also encounter a situation where raising severity of central punishment backlashes, leading to higher defection through the suppression of local enforcement. Before concluding the chapter we examine how the situation changes when we make policy with imitators instead of maximizers, and give some final remarks on the difference between the two cases. In the very end we add some ideas for further investigations of policy problems with Contributron.
3.6.1. Policy Parameters
Contributron features a central authority, which is able to check and punish agents, and it may also be supposed that the expected level of contribution is decided centrally. Although the mechanism of supervision and punishment is simple, it is still comparable to what analytical models could achieve, and is able to deliver interesting insights even at its current form. Nevertheless, there is nothing to preclude further complication of this component if desired. You might recall that in Contributron there are three so-called policy parameters: CPE, that is the amount deduced from R each time an agent is punished by the central authority (severity of punishment), CPR, the probability of central checks per turn per agent (certainty of punishment) and TR, the tax rate, the fraction of endowment that agents are supposed to contribute in each period. In principle, the central authority is able to affect behavior through these instruments, each of them influencing individual and system behavior in different ways. In this chapter we are going to concentrate on the effects and use of these three parameters.
3.6.2. Policy Statistics
One of the exported data from the executable can be used directly to assess central strategies. It is Contribution, which together with all other exports is available both at the individual level and as a population average. Here I am going to use the latter, as the focus of this chapter is set at how to maximize overall contribution. (The individual data could be more used if the objective was some kind of social policy instead.) 406 For the other two
406 Note that also although Contributron models smaller communities, when talking about policy − for simplicity − I am using taxation terminology: for example it is easier to say “tax rate” than the “expected rate of contribution”. Besides, many of the qualitative findings presented here can easily have their counterparts in larger populations. For instance, we will shortly see that the relation between TR and the net tax is similar to what has been observed at larger scales. It is worthwhile to note that at least with certain parameter settings the
- 158 - statistics I am going to use we have to make assumptions on the “costliness” of three different elements in the taxation process. First is the cost of checking an agent by the central authority, which I am going to mark with ‘cc’. Second is the cost of actually exerting punishment to an agent, denoted by ‘cp’. Finally, considering that fines can be a source of income for authorities, the fraction of the punishment deduced from R that is paid in as a fine is represented by ‘fr’. Using this notation, the first of the statistics is what I call ‘Net Income’ (of the central fund, as opposed to ‘contribution’ which is the gross income). It is given by E()**(1)***NI=−− ETR B BCPRCPEfrCPRccBCPRcp −− * ** (3.25)
Tax Fine Cost of Cost of Check Punishment
Note that CPE is normally negative.) Observe that NI in this form is only an expected value (CPR is a probability, and if we are using discrete taxation, B too). If we plug in individual Bs then it refers to individual agents, but we can also use an average B level to obtain the population average NI, (and thus the overall net income, by multiplying it with P). We can calculate the ex post value of NI (which is displayed on several figures below) from the exported statistics the following way.
NI=− con cpur** CPE fr − cchk * cc − cpur * cp (3.26)
Where ‘con’ is the exported contribution, ‘cpur’ is the number of central punishment received, and ‘cchk’ is the number of central checks. Again, if we use individual data we can have this statistic for particular agents, but if we plug in population and/or time averages we arrive at the population and/or time average of Net Income (and by multiplying it by P and/or the number of periods the total income.) The other statistic I am going to use is the ‘Deadweight Loss’ caused by taxation:
E(DW )=− B * CPR * CPE *(1 − fr ) + CPR * cc + B * CPR * cp (3.27)
Unpaid fine Cost of Cost of Check Punishment
Where the ‘Unpaid fine’ is the amount that is deduced from the agent, but not accounted for in NI as a fine. The ex-post value of the statistic is calculated as:
DW=− cpur**(1) CPE − fr + cchk * cc + cpur * cp (3.28)
3.6.3. Laffer Curves
agents of the model could be also interpreted as homogeneous groups of people, which may extend the validity of its findings to greater populations.
- 159 - Let us first see how imposing different TRs affects our statistics including NI, an eternal question of taxation policy. The first thing we must remember is that TR does not affect B when agents maximize with continuous contribution, but it does so in the discrete case. This is why it is only possible to use TR as a policy parameter when our maximizing agents face the discrete regime. When agents are homogenous, the picture we get is not very exciting, since all agents would change their Bs from 0 to 1 at the same TR level. However, when agents are heterogeneous with respect to any parameter that is included in the formula for optimal B, we encounter a different situation.
Mean Avg . Boldness Mean Avg . Boldness vs . TR Mean Avg . Contribution Mean Avg . Contribution vs . TR 1
5 0.8 4 0.6 3
0.4 2
0.2 1
TR TR 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1
Net Income Net Income vs . TR Deadweight Deadweight vs . TR 3.5 7 3 6
2.5 5
4 2
3 1.5
2 1
1 0.5
TR TR 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 Figure 50 – MAB, MAC, NI and DW of a heterogeneous population (5 income groups E={10, 20,…,50}, CPR=1, CPE=−10) of discrete maximizers as a function of TR
What we see here is that the MAB approaches 1 with discrete jumps where TR reaches the level where the particular groups switch their Bs from 0 to 1. The shape of all other statistics can be derived from this. Contribution grows gradually with TR, and falls back where a group defaults. Note that its slope between falls diminishes as there are less and less agents contributing. NI grows with contribution, and also drops at the corresponding TR levels. Although at each fall-back level the payable tax is equal to the punishment (by the definition of optimal B), NI still slumps because punishment is costly, and because only a fraction of the punishment is accounted for as income. Deadweight grows for the same reason and with the same amount at each step where NI drops. We can already notice that contribution has a maximum at a certain TR level. Depending on cc, cp, fr and the distribution of the heterogeneous parameters this can also be true for NI, while the level of TR where the maximum lies also depends upon these setting. Here are a couple of examples demonstrating the various shapes NI may show with different distributions of E and W:
- 160 - Net Income Net Income vs . TR Net Income Net Income vs . TR 0.3 0.3
0.2 0.2
0.1 0.1
TR 0.2 0.4 0.6 0.8 1 TR 0.2 0.4 0.6 0.8 1
-0.1 -0.1
-0.2 -0.2 Linear E Normal E
Net Income Net Income vs . TR Net Income Net Income vs . TR 0.1 0.15 0.05 0.1
0.05 TR 0.2 0.4 0.6 0.8 1 TR 0.2 0.4 0.6 0.8 1 -0.05 -0.05 -0.1 -0.1
-0.15 -0.15 -0.2 -0.2 Hyperbolic E RNDU W
Figure 51 – Shape of NI in response to TR (Laffer-curves) with various distributions of E and W
The fact that raising tax rate after a time diminishes tax income has been recognized by economists a long time ago. Similar curves have been called Laffer-curves, plotting the relation between tax rate and tax income. The last of the above graphs, marked “RNDU W” shows a situation where the curve is not generated by different income groups, that is all agents had the same E, but where heterogeneity has been achieved by initializing W with RNDU(0,1), fixing it and placing agents into a RCOR network. Since in this situation all agents had neighbors with different Ws, they faced different expected punishment and thus they switched their Bs at different TRs, similarly to when this variability is caused by a heterogeneous endowment. Although in these basic cases it would not be impossible to draw the approximate shapes of these curves using analytical methods, what has been told demonstrates how Contributron can be used to look for the optimal TR in much more complex situations with any desired assumptions the model can accommodate.
3.6.4. Policy Making with Severity and Certainty
Following looking at how TR can be used for maximizing contribution, we consider what CPE and CPR can do for a higher cooperation.
3.6.4.1. The Classical Setup
Recall from the first part how Economics of Crime attempted to advise policy makers on the optimal certainty and severity of punishment for efficient enforcement of pro-social
- 161 - rules. Those models usually assumed maximizing actors, incapable for the private enforcement of public rules. Here we attempt to reproduce their results. The figure below shows what happens to NI and DW when we vary CPE in circumstances similar to the above described.
Net Income Deadweight
0.5 1.3 0.25 1.2 CPE -3. -2. -1. 1.1 -0.25 CPE -0.5 -3. -2. -1. 0.9 -0.75 0.8 -1
Figure 52 – Net Income and Deadweight in response to different levels of CPE (with continuous maximizers)
What we can see here is that both statistics appear to be monotone in CPE (where B<1), which is easy to show by plugging in the formula for optimal B into NI and DW, and which also yields their limiting levels. At the same time if we try to move CPR instead, we arrive at the following.
Net Income Deadweight 1 0.2 0.15 0.8 0.1 0.6 0.05 CPR 0.4 0.25 0.5 0.75 1. -0.05 0.2 -0.1 -0.15 CPR 0.25 0.5 0.75 1. Figure 53 - Net Income and Deadweight in response to different levels of CPR (with continuous maximizers)
It is similarly easy to show that DW will be monotone (and linear) in CPR when B<1. The more interesting is that NI gives a maximum with CPR (that is certainty). The shape of NI results from the following. While CPR is low, B is not affected by it, thus we got a linear interval whose slope is determined by cc and cp. Then B begins to respond and NI to grow, but after a certain level, CPR will not be able to press down B enough to counterweight the growing cost of checks, and NI begins to shrink again. (We must add that by the diminishing B the income from fines also decreases.) Because we use a simple setup, it is possible to derive the optimal CPR level, where NI is maximal.
- 162 - ETR* CPRˆ =− (3.29) 2*CPE * cc
Recall that orthodox models of Economics built on the foundation of maximizing agents proposed severe punishment while some of them looked for optimal levels of certainty because they supposed that surveillance was costly. This result has just been reproduced. To go just one step further, we can suppose that we have a social planner, who in addition to maximizing tax income, might also be interested in minimizing deadweight. Say he has a utility function in which −DW has a weight of ε and NI a weight of (1− ε). By plotting this social utility function for the above situation with ε=0.35 we get the graph below.
Social Utility CPR 0.25 0.5 0.75 1.
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
Figure 54 – Social utility function combining Net Income and Deadweight
We can see that the optimum has shifted backwards. (Observe that applying the social utility to try to find an optimum for CPE will not work since NI grows while DW shrinks with CPE, therefore the social utility is also monotone with any ε.) The analytical value of optimal CPR in this case is
ˆˆ CPRSP = CPR*(1)−ε (3.30)
That is smaller than CPR hat. It is instructive to see how applying the corresponding optimal CPR at different CPE levels improves the net income relative to a flat CPR level.
- 163 - Net Income CPR
1 J N
NI CPR =0.75
0.5
NI Opt . CPR
CPE -3.5 -3 -2.5 -2 -1.5 -1 -0.5 CPR =0.75
-0.5 Opt . CPR
-1
Figure 55 – NI with a flat CPR (=0.75), NI with the optimal CPR for the corresponding CPE levels, the 0.75 CPR line, and the optimal CPR that maximizes NI
This is basically just another aspect of the above facts. Notice that the line for NI produced with a flat CPR touches the other line for NI created by applying the optimal CPR to each CPE level exactly where the flat CPR level is just optimal (that is where the green lines intersect).
3.6.4.2. Static Peer Penalty
So far for CPR and CPE we have only dealt with the simplest setup conceivable: one drive (maximization), homogenous population and no peer punishment. Now we move a little bit ahead and allow for peer penalty with default initialization but no updating for W.
Net Income Deadweight 0.6 CPE -3. -2. -1. 0.5 0.588
0.4 0.586
0.3 0.584
CPE -3. -2. -1. 0.582
Net Income Deadweight
0.7 0.7 0.6 0.65 0.5 0.4 0.6 0.3 0.2 0.55 0.1 CPR CPR 0.25 0.5 0.75 1. 0.25 0.5 0.75 1. Figure 56 – NI and DW in a population of continuous maximizers with PPE<0
- 164 - The most important difference we realize is that in this case DW is not necessarily monotone decreasing in CPE, not even monotone any more (which can also be shown from the formulas for B and DW). It implies that at least with certain parameter settings a social optimum can be found for CPE (i.e. severity), just as we have seen for CPR, and as it is shown below. (It must be added, though, that the formula for DW shows that this optimum is only local, because when CPE gets very large DW converges to a minimum.)
Net Income Deadweight Social Utility 0.98 0.2 0.96 -0.648 0.94 0.1 CPE 0.92 -5. -4. -3. -2. -1. 0. CPE CPE -5. -4. -3. -2. -1. 0. -0.652 -5. -4. -3. -2. -1. 0. 0.88 -0.1 0.86 -0.654
Figure 57 – Maximizing social utility with CPE in a population of maximizers with PPE<0
Besides, we still have the familiar optimum with CPR. Although it is still possible to come up with a formula for optimal CPR, it is much more complicated than in the preceding case without PPE. Moreover, it also depends on local W levels non-linearly, which leaves us with simulation as the only viable way to examine its features and reactions.
3.6.4.3. Dynamic Peer Penalty
This is even truer if we go yet another step further and let W change. Allowing for WUDC>0 (that is supposing that central punishment facilitates local punishment), and WUDP>0 (which means that it is easier to punish when one is surrounded by active punishers), we can observe the following in response to CPR.
Net Income Net Income vs . CPR Mean Avg . Boldness Mean Avg . Boldness vs . CPR Mean AvgMean . Watchfulness Avg . Watchfulness vs . CPR 0.2 1 0.12 0.8 0.15 0.1 0.6 0.08 0.1 0.06 0.4 0.04 0.05 0.2 0.02 CPR CPR CPR 0. 0.2 0.4 0.6 0.8 1. 0. 0.2 0.4 0.6 0.8 1. 0. 0.2 0.4 0.6 0.8 1. Figure 58 – NI, MAB and MAW in response to CPR in a population of maximizers when CPE<0, WUDC>0 and WUDP>0
I have plotted with NI MAB and MAW because of the special connection between central and local punishment. We can observe that at a certain CPR level MAB begins to fall suddenly at the same time when MAW starts to increase. The reason for the abrupt increase of the latter is that more frequent central checks facilitate the ignition of W, which in turn assists central punishment in depressing B. After a certain level, though, B does not drop fast enough so that the additional income can counterweight the loss from the cost of more frequent checks, which is why NI starts to fall again. Thus we have the usual maximum in CPR, this time, however, totally incalculable via analytic means. Note also that W level also has a
- 165 - maximum, because the drop in B caused partly by CPE weakens the positive feedback mechanism as we already know. In the last experiment we applied central and local punishment simultaneously. (CPE and PPE < 0.) Let us now check what we find if we suppose that agents do not care about central punishment directly at all, that is it only influences behavior via its ability to generate a punishment norm (PPE=0).
Net Income Net Income vs . CPR Mean Avg . Boldness Mean Avg . Boldness vs . CPR Mean Avg .Mean Watchfulness Avg . Watchfulness vs . CPR CPR 1 0. 0.2 0.4 0.6 0.8 1. 0.5 -0.05 0.8 0.4 -0.1 0.6 0.3 -0.15 0.4 0.2 -0.2 0.2 0.1 -0.25 CPR CPR 0. 0.2 0.4 0.6 0.8 1. 0. 0.2 0.4 0.6 0.8 1.
Figure 59 - NI, MAB and MAW in response to CPR in a population of maximizers when CPE=0, WUDC>0 and WUDP>0
Not surprisingly, we find the optimum in CPR at a different place. Of course, amongst such complex circumstances, the position of this optimum can only be acquired by simulation. It is instructive to see how to do this, also because with other parameters of interest the position and movement of optima could essentially be found the same way.
Net Income vs . CPR for different values of CPE Net Income vs . CPR and CPE Net Income
0.6 CPE = -2. -1.9 -1.8 -1.7 -1.6 -1.5 0.4 -1.4 -1.3 -1.2 -1.1 -1. -0.9 -0.8 -0.7 0.2 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.6 CPR 0.2 0.4 0.6 0.8 1
0.40. -0.2 -2. 0.2 -1.9 -1.8 Net Income -1.7 0 -1.6 -1.5 Opt . CPR -0.2 -1.4 0.9751. 0.8 -1.3 0.9250.95 0.9 -1.2 0.850.875 0.80.825 0.75 -1.1 0.775 0.75 -1. 0.70.725 0.675 CPE 0.65 -0.9 0.625 0.7 0.6 0.575 -0.8 0.55 0.525 0.5 0.65 -0.7 0.475 0.45 0.425 -0.6 0.4 0.375 CPR 0.35 0.6 -0.5 0.325 0.3 0.275 -0.4 0.25 0.225 0.55 0.2 -0.3 0.175 0.15 0.125 0.1 CPE -0.2 0.075 0.05 -1.75 -1.5 -1.25 -1 -0.75 -0.5 -0.25 -0.1 0.025 0. 0.45
Figure 60 – NI in response to changing CPR at different CPE values (WUDC>0 and WUDP>0). The lower graph on the right shows the (locally) optimal CPR level at different CPEs (that is where the peaks are on the graph above).
Observe that the optimal CPR appears to be non-monotonic in CPE, unlike in the case of maximizers as can be seen in equation (3.29) and Figure 55. In other words if we have a population involving punishers raising severity first requires a higher, later a lower certainty in order that we maximize the net tax income. The other thing to mention is that MAW reaches much higher levels, and also it does not turn around since here CPE does not interfere with B. With a less strict central punishment a higher level of peer punishment is attainable. To see the effect of CPE in this situation get a look at the following.
- 166 -
Net Income Net Income vs . CPE 0.2 Mean AvgMean . Boldness Avg . Boldness vs . CPE Mean AvgMean . Watchfulness Avg . Watchfulness vs . CPE 0.18 0.86 0.2 0.84 0.16 0.15 0.82 0.14 CPE 0.1 -2.25-1.875-1.5-1.125-0.75-0.375 0. 0.12 0.78 0.05 0.76 CPE 0.74 CPE -2.25-1.875 -1.5 -1.125-0.75-0.375 0. -2.25-1.875-1.5-1.125-0.75-0.375 0. 0.08
Figure 61 - NI, MAB and MAW in response to CPE in a population of maximizers when CPR=0.25, WUDC>0 and WUDP>0
Quite logically, MAW goes down as CPE grows (in absolute value). Less logically, MAB at the same time displays a hump shape. This is actually an interesting situation: applying more severe punishment increases the level of defection. Knowing the model and the parameters it is not too difficult to see why it is so, but it calls attention to that policy can backfire if decision makers ignore social effects. The cause of this effect is that a higher CPE keeps B under the level necessary for ignition for a longer time. Although when WUDP>0 (and CPE=0) B can reach high peak levels as we have seen with oscillations, its average can be quite low because W propelled by the positive feedback returns it to its floor level quickly. In contrast in this case, if anything, CPE hinders the effective suppression of B by holding it at a moderate level and at the same time by making W harder to ignite. Nevertheless, if CPE is allowed to get really high, it will keep B low by itself, resulting in the hump shape we have just experienced. Mark also that here even NI has a U shape, despite that in all our previous experiments it was monotone in CPE. It further emphasizes the existence of the policy-trap: more severe punishment can result in not only higher defection, but also less income.
3.6.5. Policy-Making with Imitators
At this point the road is open to investigate the above presented statistics and optima for the most diverse communities and environments. Naturally, there is no room here to go much further, which is why I will only include one more example where we abandon even maximization for imitation.
Net Income vs . CPE for differentNet Income values of BUSC BUSC = Net Income vs . CPE and BUSC 0.6 0. 0.1 0.2 0.4 0.3 0.4 0.2 0.5 0.6 CPE 0.7 -3 -2.5 -2 -1.5 -1 -0.5 0.8 -0.2 0.9 1. -0.4 -0.6 0.5 -0.8 0 0. Net Income 0.10.1 Net Income vs . BUSC for different values of CPE -0.55 0.2 Net Income CPE = 0.3 0.6 -3. -3. -2.7 -2.7 0.4 -2.4 -2.4 0.5 0.4 -2.1 -2.1 BUSC -1.8 -1.8 0.6 0.2 -1.5 -1.2 -1.5 0.7 BUSC -0.9 -1.2 0.2 0.4 0.6 0.8 1 -0.6 CPE -0.9 0.8 -0.2 -0.3 -3.33067 -0.6 0.9 -0.4 -0.3 -3.33067 × 10 -161. -0.6 -0.8
Figure 62 – NI on a population of imitators (BUSC=0…1, RCOR network) in response to CPE
- 167 -
In this figure we can see how NI changes on homogenous populations consisting of imitators with different BUSC parameters ranging from 0 (payoff-biased) to 1 (average- biased) in each population. In the second chapter we have already familiarized ourselves with imitators. Remember that payoff-biased imitators can effectively mimic individual maximization in favorable circumstances. On the contrary, completely average biased imitators (BUSC=1) are absolutely not affected by punishment. What we can see on the above graph is a consequence of this: for average-biased agents the net income changes linearly (since only the amount of fine grows proportionally with CPE. For payoff-biased ones, however, B reacts to the punishment, which for weak punishment results in high, and strong punishment low B. When CPE is still able to press B down the slope of NI is steeper than with high BUSC. When CPE is high, though, it cannot suppress B further because it is already close to 0, and this is why not only the tax, but the income from fine also increases slowly, NI giving a flatter slope than with average-biased agents.
Net Income vs . CPR for different values of BUSC Net Income BUSC = Net Income vs . CPR and BUSC 0.5 0. 0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.3 0.7 0.8 0.9 1. 0.2
CPR 0.5 0.2 0.4 0.6 0.8 1 1. Net Income 0.4 0.9 Net Income vs . BUSC for different values of CPR 0.8 0.3 Net Income 0.7 CPR = 0.5 0. 0.6 0.1 0.2 0.0. 0.5 0.3 0.1 CPR 0.4 0.4 0.2 0.4 0.5 0.3 0.6 0.4 0.3 0.3 0.7 0.5 0.8 0.6 0.2 0.9 BUSC 0.7 1. 0.8 0.1 0.2 0.909 0. 1. BUSC 0.2 0.4 0.6 0.8 1
Figure 63 – NI on a population of imitators (BUSC=0…1, RCOR network) in response to CPR
Examining how NI reacts to CPR, we again see that with BUSC=1 it is linear. But this figure reveals two more interesting features. First, when agents are sufficiently payoff-biased, we again have the familiar maximum with CPR that we already know from maximizers. Here of course, there is no way to tell where it will actually occur without simulation. The other instructive observation is that similarly to CPE there is a special CPR level where all population types yield the same NI. (Check it on the upper right projection.) To use this CPR can be useful for example when the policy-maker is not sure what kind of population he is dealing with. The cause is quite simple. At this particular level of CPR the expected punishment is such that with respect to the expected change in his R the B level of the agent is indifferent, which is why the average B remains close to 0.5 even if the agents are to some degree payoff-biased. We will be able to observe this feature with any kind of parameters as long as there is such a CPR level between 0 and 1.
- 168 - Net Income vs . TR for different values of BUSC Net Income BUSC = Net Income vs . TR and BUSC 1 0. 0.1 0.2 0.8 0.3 0.4 0.5 0.6 0.6 0.7 0.8 0.4 0.9 1. 0.2 TR 1 0.2 0.4 0.6 0.8 1 0.75 1. Net Income 0.5 0.9 Net Income vs . BUSC for different values of TR 0.25 0.8 Net Income 0 0.7 TR = 1 0.1 0.6 0.2 0.0. 0.3 0.1 0.5 TR 0.8 0.4 0.2 0.5 0.3 0.4 0.6 0.6 0.4 0.7 0.5 0.3 0.8 0.6 0.4 0.9 BUSC 0.7 1. 0.8 0.2 0.2 0.909 1. 0.1 BUSC 0.2 0.4 0.6 0.8 1
Figure 64 - NI on a population of imitators (BUSC=0…1, RCOR network) in response to TR
This figure, displaying the effect of our third policy parameter, TR, shows another phenomenon that we could not observe so far: with low BUSC we have a hump shaped NI in a homogenous population. (Recall that with discrete maximizers we have always needed some kind of heterogeneity in the parameters and variables included in the formula for optimal B, because otherwise the whole population would jump at the same TR level between 0 and 1, while continuous maximizers were not sensitive to TR.) Because we were using discrete taxation here the best TR level is still either 0 or 1 to maximize individual income. Nevertheless, because the income is stochastic, there is a positive probability for that during a limited time other strategies will do better, which can move the MAB out of the optimum. However, the probability that an inferior strategy does better than the optimal and this is why this displacement of MAB gets smaller in probability when TR is farther from the value that divides between optimal 0 and 1. This is the reason for the gradual transition of B between optima and consequently the hump shaped NI.
3.6.6. Individual Maximization and Payoff-Biased Imitation
This is a good place to underline an important difference between individual maximization and payoff-biased attainment of the optimum. The above phenomenon could never be observed by with maximizers, because what they consider is the expected value of income, which is always the same, regardless of stochastic events. The evolutional emergence of the optimal strategy, however allows for that inferior strategies do better than the optimal one for a limited time, which especially coupled with a short term memory can divert the average behavior from the strict optimum. The figure below illustrates this proposition with comparing the gradual transition of payoff-biased imitators with the sudden shift of maximizers in MAB between low and high optima.
- 169 - Mean Avg . Boldness Mean Avg . Boldness vs . TR Mean Avg . Boldness Mean Avg . Boldness vs . TR 1 0.8
0.8 0.6 0.6
0.4 0.4
0.2 0.2
TR TR 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9
Figure 65 – MAB moving between optima in response to TR gradually with homogenous payoff-biased imitators (left) and shifting suddenly with maximizers (right)
3.6.7. Summary of Findings
● In a discrete regime with maximizers the net contribution can display hump- shaped forms as a function of tax rate as it can be observed in real life taxation. It requires that agents be heterogeneous in the parameters determining optimal defection, or that we suppose that agents can or be willing to punish each other differently. The shape of this so-called Laffer-curve depends upon the distribution of what causes the heterogeneity.
● Supposing that agents are maximizers who are affected only by the central policy, Contributron reproduces the findings of classical economic models of crime and taxation proposing high severity and an optimal level of certainty of punishment. This optimum depends positively on the endowment, tax rate, and negatively on the severity of punishment and the cost of central checks.
● Together with the net income, a social utility function combining overall (or average) net income and deadweight of taxation can have an internal maximum with respect to the certainty of punishment. With maximizing agents this level is lower than the optimum when the objective of the social planner is simply to maximize overall contribution.
● Allowing for fixed peer punishment, we can find (local) optima for the severity of punishment in social utility. At the same time we still have the optimum for the certainty. In this case, however, we have to use simulation to obtain the actual location of the maxima.
● Considering the norm supporting role of central authority the certainty of central punishment affects the location of optima through supporting local punishment, too. In this situation, increasing the severity of central punishment without taking into account social effects can entail a rise in the probability of defection through suppressing local punishment. This policy trap can manifest also in a shrinking net income.
● There is a special level of certainty of central punishment, where the net income is approximately the same for all kinds of imitators.
- 170 - ● Unlike the outcome of individual maximization, the overall defection level emerging due to the evolutional process resulting from payoff-biased imitation is influenced by stochastic events. Consequently, we can observe Laffer-curve like phenomena (hump shaped NI with TR) even when agents are homogeneous.
3.6.8. Further Possibilities
Again, here we have been able to touch upon only a thin slice and the most basic examples of policy issues that can potentially be handled by Contributron. Here are a couple of ideas for more involved analyses under the umbrella of policy issues. Firstly, one could find other statistics to optimize than Net Income, Deadweight or the Social Utility. Secondly, it would be interesting to see how different optima shift by moving the numerous parameters and settings of the model, say to examine how population affects them. Thirdly, it is easy to imagine situations where the costs of different stages of the taxation process are not flat but depend upon endogenous variables. For example we could suppose that the cost of punishment is higher when there are many defectors or few punishers. Fourthly, policy planning does not necessarily have to stop at maximizing some measure of overall contribution. The objective could be social, aiming at for example improving the conditions of certain agent groups. Fifthly, the statistics we have used to assess the impact of different policies can be used with other settings of the model that is to check how different network and agent configurations affect the efficiency of the contribution process without any reference to policy making. The model is already able to house many of these problems, on the one hand because agents can have individual policy parameters, and on the other because all the data exports are available at the individual level, too.
3.7. Experimental Connection
As it was mentioned, the aims of Contributron include aiding experimental economists with insights into the mechanisms that govern human behavior at the individual and group level, showing how various micro-level rules result in different macro-scale outcomes and suggesting new directions in real-life experimental investigations. Although our final goal is a better understanding of human behavior, conducting real-life experiments can be difficult for multiple reasons as described in the first part. For example if we want to obtain abstract and exact knowledge, we are compelled to set up artificial experiments to oust as much of the unintelligible and haphazard influences of the real world as possible. This, however, unavoidably distorts the behavior of the subjects, too. Observation perturbs the observed,407 which puts a new kind of uncertainty into the knowledge acquired this way. The second reason is of course the costliness of such experiments. Nowadays researchers seeking to publish their results are bound to use real stakes in their experiments. This imposes a rather hard limit on the number of topics to focus at, the number of participants and the replications of experiments that is needed for statistical inference. In this final chapter first we demonstrate how the parameters and other settings of Contributron can be calibrated to empirical data. After adjusting the model to correspond most closely to real life experimental setups and the agent pool to the participants, I will show how it can be used to augment our understanding of experimental results, how it allows us to
407 Just like in quantum physics…
- 171 - carry out simulated experiments quickly, simply and cheaply and how it can help us to formulate new, testable hypotheses. For this end we are going to examine the effects of altering group size, turning reshuffling on and off that is the difference between stranger and partner treatments in experimental terminology, and we will allow for convergence in the propensity to punish, an issue largely neglected by real-life experiments. We find that these three factors have an effect on contribution that springs from the same roots. Basing upon our findings we are going to formulate some testable hypotheses. Finally we go back to the familiar question of certainty and severity, this time from the perspective of peer punishment, and we are going to inspect how different combinations of W, PPE and BUDP affect contributions. At the end we will see how Contributron can be used to find optimal mixes of these parameters, provided that there is a constraint on increasing them simultaneously.
3.7.1. Calibration
When one intends to use Contributron to simulate concrete setups, before running the model the first thing to do is to collect data on agent behavior and network structure in real experiments. Fortunately, the literature supplies us with sufficient information to estimate parameters and determine settings for the model so that it is able to faithfully regenerate the behavior of real subjects. In what follows I am relying on the following works: Bowles and Gintis (2000b) (BG), Carpenter (2004b) (C), Fehr and Gächter (2000, AER) (FGA), Fehr and Gächter (2002, Nature) (FGN) and Falk (2004) (F). All of them conducted very similar PG experiments. Let us now try to obtain estimates for the parameters of our model.
- 172 -
3.7.1.1. Estimating BUR
The following graphs are from (FGA):
Figure 66 – Results of a PG game experiment, showing the evolution of average contribution. In periods indicated by the filled blobs optional (and costly) peer-punishment was available, while in the rest there was no punishment. Stranger (left) and Partner (right) treatments.
We know that without punishment the Nash-equilibrium of the game is zero contribution for all agents. We can observe on all of the above graphs that it is indeed the case that the average contribution level converges to zero. Note also that it does not jump to zero. If we consider the corresponding situation in Contributron, without punishment (and supposing there is no noise) the only drive influencing AB is BUR. Thus we can fit (by OLS) a geometric trend onto the no-punishment data points of the above graphs, whose quotient will give us an estimation 408 of (1−BUR). (The two quotients of the same treatment are averaged before BUR is calculated.) This way we obtain the following estimates for both the contributor type and as a population average in a homogeneous population:
408 In fact the problem is a little bit more complicated. Supposing that we have free-rider and contributor types, the free-riders contributing zero regardless the contribution of their peers (as shown on Figure 68), we must divide the above contribution values with the relative share of the contributor types to get their contributions. If we calculate the BUR of the contributors from the modified values, though, we get the same estimates as if we were supposing a homogenous population and using the unmodified values.
- 173 -
Contribution 20 17.5
BUR(Coop, Pop), Partner = 0.1154 15 12.5 10
7.5 BUR(Coop, Pop), Stranger = 0.16 5 2.5 Period 2 4 6 8 10
Figure 67 – Estimating BUR from empirical data
Not surprisingly, for subjects playing with strangers the egoistic motive appears to be stronger.
3.7.1.2. Estimating BUS
Next, we need to estimate BUS. Fortunately, (F) supplies us with information on conditional contribution. Consider the following figure.
Figure 68 – Conditional cooperation in PG situations
Conditional contribution is captured in Contributron by BUS, which modifies the willingness to contribute basing on the average contribution level of neighbors. Observe above that even the conditional contributor type contributes less than the average in the group.409 We can suppose that this is an equilibrium level between egoistic motives pulling
409 In some experimental papers it is stated that cooperation is broken down by the presence of free-riders, who cause the conditional cooperators to adjust their cooperation level downwards continuously until the whole group ends up in complete defection. Although the above data says that free-riders indeed have a great part in this process, it also tells us that defection would prevail even if the population would consist of exclusively conditional cooperators.
- 174 - players towards complete defection and a drive towards the average. (Similarly to what we have seen on Figure 19.) By estimating the slope of the line of conditional cooperators we have that it is about 0.75. The same for the population average is 0.456. Thus, we have
BUSCoop, Partner = 0.115*0.75/0.25 = 0.345 BUSPop, Partner = 0.155*0.456/0.544 = 0.13
BUSCoop, Stranger = 0.16*0.75/0.25 = 0.48 BUSPop, Stranger = 0.26*0.456/0.544 = 0.134
Besides, we can immediately see that
BUSFree-rider, Partner = BUSFree-rider, Stranger = 0
Another important clue is that free-riders tend to behave completely selfishly that is they play the Nash-response regardless the behavior of other members of the group. This is why for them we will use
BURFree-rider, Partner = BURFree-rider, Stranger = 1
3.7.1.3. Estimating BUDP
With BUDP we are even luckier. On the one hand (BG) (p11, p13) finds evidence for their hypothesis
“Shirkers respond to punishment by increasing their contribution in the next round.”
On the other hand in (FGA) we find that
„In 89 percent of these cases the punished subject increased g immediately in the next period with an average increase of 4.6 tokens. In the Stranger treatment we have 368 such cases. In 78 percent of these cases g, increased in the next period by an average of 3.8 tokens. These numbers suggest that actual sanctions were rather effective in immediately changing the behavior of the sanctioned subjects.”
(Where g is the individual contribution.) Considering that the players had 20 tokens as an endowment in each period, we can calculate the BUDP for those who reacted to punishment and we can also calculate a population average using the percentages the authors deliver. Thus we have:410
410 Note that experiments are conducted in an extremely information intensive environment. All information thought to be relevant to change behavior is readily supplied by the experimenters and all others are filtered out.
- 175 -
BUDPCoop, Partner = −4.6/20 = −0.23 BUDPPop, Partner = −4.6*0.89/20 = −0.2
BUDPCoop, Stranger = −3.8/20 = −0.19 BUDPPop, Stranger = −3.8*0.78/20 = −0.148
And considering that free-riders always play Nash, we can also suppose that
BUDPFree-rider, Partner = BUDPFree-rider, Stranger = 0
3.7.1.4. Estimating PPE
I have already mentioned that willingness to punish seems to be sensitive to the price of punishment. In most PG experiments punishment is costly; moreover it usually has an increasing marginal cost. By adjusting this marginal cost the experimenter can effectively control the punishment delivered to shirkers, the counterpart of PPE, as it is shown for example in (C).411 This is why we could have PPE as a free parameter, but to get closer to a real setting we can also have an estimate for it from (FGN), where we find the following data.
Figure 69 – Expenditure on punishment in a PG experiment
This is the reason for high parameter estimates and low inertia. In real-life people face a much more complex environment and influences reach them more indirectly, resulting in slower and noisier adaptation. Another characteristic feature of simulating these experiments is that it is very clear what to be taken as one period, and how many of them are to be simulated. When we are talking about social interaction outside the lab, it is much more difficult to decide what should be represented by a turn in the model: one day, one occasion of interaction, etc… This is why it is probably practical to take the model towards continuous dynamics by setting parameters low and carrying out a large number of simulated periods (smooth simulation). Thirdly, what also makes the model well fit to these experiments is its synchronous updating method. In addition to the above mentioned argument for using smooth simulation, it also can be useful to decrease the gap between the outputs of synchronous and asynchronous updating. 411 Remember that PC is not the same cost of punishment that I am talking about above since it is not directly considered in updating W (indirectly it is through WUS). PC is the prestige attached to being a punisher, which makes the him a success to be followed or a sucker to be avoided.
- 176 -
Calculating the average spending on punishment and combining it with the actual price of punishment, we can have an estimation on peer penalty, PPE = −2.06 (with an endowment of 20). We could even obtain an estimate for the average W level in the population by putting this PPE with the final B level from the same article (=0.2 =(20−16)/20, where 16 is the final average contribution in the punishment case) into the formula for optimal B in Contributron, which gives approximately 0.4. This, however depends on many things, most importantly on whether 16 was really the optimal contribution level, of which we cannot be sure since the B of the various agents have been driven by many other motives then BUR. This is why I will use the default initialization in the forthcoming experiments that is an average W level of 0.5.
3.7.1.5. Determining Further Parameters
The rest of the parameters are fairly easy to determine. E=20, as this value was used in experiments that made obtaining our estimates possible. TR=1, as in PG games in principle the whole endowment should be contributed. All central parameters are 0, as there was no central authority. BUSC=1, since subjects were not informed about the successfulness of their peers, but they knew about each other’s cooperation behavior. (The information conditions of the experiments were strictly controlled, and players were isolated from each other except for the information on contributions.) Noise is also taken to be zero to reflect the information rich and sealed environment. By default, all updating parameters for W are zero (Where we will use WUS>0, WUSC is set to 1, supposing that only the actual punishment behavior is revealed.) Finally, on Figure 66 we find that with stranger treatment the average contribution does not converge to full even with punishment. Moreover, it happens while agents still punish each other, and they even react to direct punishment. FGA writes (p992) that the number of cases in which agents punished each other was even higher in the stranger treatment, while they also reacted to it directly in the following period412. However, in this case it seems that agents did not perceive punishment as a warning that future punishment is more probable, and consequently on the long run they reverted to higher defection. This is a new phenomenon relative to the other treatments that requires adjustment of the parameters. We still must have BUDP (because the punished still react directly) and we cannot estimate a separate BUR, thus the modification is best done using BUNM to capture the increased propensity to defect.
3.7.1.6. Weaving the Net
The network setup conforms to a standard experimental design. More closely, it is what has been used in (FGA): 24 agents divided up into 6 four-person groups. Originally the small groups are connected fully inwards, but are completely isolated from each other. The blockNetwork[] Mathematica function introduced in chapter 3.5 has been used to produce the super-network with FULL sub-groups. In the partner treatment the RANDOMIZE shuffle type has been used, shuffling the agents randomly only before the first period, while stranger treatment has required the RERANDOMIZE variant, shuffling the agents across groups in
412 See the quotation on page - 175 -.
- 177 - each period, just like in the real-life experiments.413 Although our aim is to reproduce real-life settings the closest possible, simulations enables us to overcome some of their shortcomings. One such improvement is that I have been able to run much more sessions (usually 100 replications with different seeds) than what real-life experiments can possibly handle. The number of sessions performed by them was around 3.
3.7.1.7. Comparing the Output
By plugging the parameters obtained above into the model, and using a homogenous population, we get the following.
Plot of Avg . Contribution Plot of Avg . Contribution 20 20
17.5 17.5
15 15
12.5 12.5
10 10
7.5 7.5
5 5
2.5 2.5
Period Period 2 4 6 8 10 2 4 6 8 10
Plot of Avg . Contribution Plot of Avg . Contribution 20 20
17.5 17.5
15 15
12.5 12.5
10 10
7.5 7.5
5 5
2.5 2.5
Period Period 2 4 6 8 10 2 4 6 8 10 Figure 70 – Simulated contributions in Partner (right) and Stranger (left) treatments with (above) and without (below) punishment (compare with Figure 66)
3.7.1.8. Acquiring Population Proportions
Human populations, however, are usually not homogeneous. This is why I have given above different estimates to parameters for different types. There are several sources in the literature assessing the prevalence of different types. Estimates vary depending on the actual subject pool and definition of the types, but there is a rough picture that can be inferred. Players tend to differ in the two main dimensions of Contributron: they can be free-riders or contributors (different B updating) and punishers or non-punishers (different W updating). There is a significant percentage of the people in each combination. Basing on several papers414 I have used the following proportions in my simulations.
413 At first sight it might be a bit strange that instead of using a single group and multiple runs (which would seem simpler in simulation) I still copy the the network structure so faithfully. The reason is that with heterogeneous agents it is not indifferent how the different agent types are distributed between groups. 414 (F) says that 32% of the people are free-riders (see on Figure 68), (FGA) on the one hand finds 11% in the partner and 22% in the stranger treatment who does not react to punishment directly, and 20% in the partner and
- 178 -
Punisher Non-punisher
Contributor 12 (50%) 6 (25%) 18 (75%)
Free-rider 4 (17%) 2 (8%) 6 (25%)
16 (67%) 8 (33%)
Table 7 – Agent-type proportions used for simulating heterogeneous populations
We have already seen how the parameters for free-riders and contributors differ. Between punishers and non-punishers the only difference is in their W level, which is 0 for non-punishers, and proportionally increased for punishers from the default population average of 50%.
3.7.2. Group Size Effect
Having determined the parameters we are now ready for using the model. One of the most widely debated questions of experimental studies is that how willingness to contribute is affected by group size. The so-called Olson hypothesis415 proposes that contribution is lower in large groups. The strongest argument for this is that when there are several players in the position of delivering punishment to the defectors, people are more liable to free-ride on the secondary public good that is the punishment, leading to higher defection. Another reason could be that such groups are less closely knitted, which however not necessarily has an effect in the artificial connections of experiments (That is even in real life experiments, where the bonds between players last only for the duration of the game.) Empirical data, though, does not seem to support this hypothesis.416 This is why one of the foci of the chapter is to examine how varying group size affects contribution.
53% in the stranger treatment who had not contributed at all when there was no punishment. (C) gives a good classification of types supplying the following percentages:
Punish Contributors Punish Free-riders Not Punish Contributor 0% 30,5% 15,28% Free-rider 5.6% 31.9% 16.6%
In Falk et al. (2001) there are 39% who does not punish and 61% who does, out of this latter 42% cooperates and 19% defects. Unfortunately it is not possible to infer how many of the non-punishers cooperate and free-ride. The definition of free-rider also varies: for (F) and (FGA) it is those who do not contribute at all in a minimum number of periods when there is no punishment, while (C) defines them as under-average contributors (and probably this is why he gets such a high percentage). Note that in the present form of Contributron agents cannot punish for spiteful reasons like free-riders who punish contributors. This type, though, appears to be the smallest of all. (Moreover, it also depends upon the definition of contributor: agents in Contributron are able to punish partial contributors). 415 See e.g. in (F). 416 In (F) we find data and references to studies showing that in larger groups the per capita contribution tends to be even larger than is small ones. (BG) also finds that „members of large teams punish more in terms of the average level of punishment”. It cites further references showing that group incentives may work in larger
- 179 -
3.7.2.1. Reshuffling
We have also seen that partner and stranger treatments are frequently distinguished since it is hypothesized that reshuffling agents will significantly alter motives. The reason for it in the first place is that in the stranger treatment participants cannot expect that their (or their fellow members’) future income will be higher due to their punishment and they also do not have to be afraid of retribution. The difference between these two treatments is the other question we start off with.
Contribution Contribution Contribution with Different Group Sizes Compensated Contribution with Different Group Sizes Compensated 20 20
H L H L 17.5 17.5 2x12 2x12
15 15 3x8 3x8
12.5 12.5 4x6 4x6
10 10 6x4 6x4
7.5 7.5 8x3 8x3
5 5 12 x2 12 x2
2.5 2.5
Period Period 2 4 6 8 10 2 4 6 8 10
Figure 71 – Average contribution with different groups sizes (using compensated punishment). The original partner treatment (right), and the same with reshuffling agents in each period (left)
Above the 24 agents are divided up into different size sub-groups ranging from 2 to 12. Naturally, if we only modified this, contributions would be larger simply because in a larger, fully connected network there are more neighbors, consequently more punishment to each agent. Because we are interested in the structural effects only, I have compensated in the severity of punishment both in PPE and BUDP proportionally to the number of neighbors. (As shown in the first chapter of this part.)417 What we find is that even after this correction, average contribution has been higher in larger groups, echoing the observations of the empirical studies under footnote 416. To find a reason, I have run the simulation with two treatments. First with the original partner setup: partner parameters and shuffling the agents only before the first period, then with the same parameters, but with reshuffling in each period. The two outputs are shown above, while the difference between them can be seen below.
groups, too. In addition, Carpenter (2004a) reviewing the literature concludes that “contributions do not fall as groups become larger and, if anything, they tend to increase.” 417 Compensating PPE in real-life experiments requires only to set a different price for punishment, while lower BUDP in a larger population can reasonably occur because of subjects are interested in the proportion of their peers condemning their behavior, rather than their absolute value.
- 180 - Difference in Contribution Between Treatments with Different Group Sizes Compensated
1.2 H L 2x12 1
3x8 0.8 4x6
0.6 6x4
0.4 8x3
0.2 12 x2
Period 2 4 6 8 10
Figure 72 – Difference between the contributions of continuously reshuffled and only once shuffled treatments with different sized sub-groups
What we find here is that similarly to increasing group-size, reshuffling boosts contribution as well, and it does more so in smaller sub-networks. Basing on our previous experience with random and fixed networks it is not terribly difficult to find the reason behind this phenomenon. In smaller groups without reshuffling the amount of punishment the distinct defectors face is much more diverse than in large ones, simply because there are less neighbors to average over. Because of this, in smaller groups punishers punish agents whose contributions are already high, instead of those with a higher defection level on whom punishment could lead to a higher growth in overall contribution. On the whole, in larger groups both defectors and punishers face a mix of the other kind closer to the population average, and this causes a better utilization of punishment. Reshuffling, on the other hand, mixes up punishers with shirkers dynamically, leading to an improvement in contributions for much the same reason, and it takes larger effect on smaller groups, where agents were more separated from each other. 418 There are two predictions coming from this finding. Firstly that even controlling for the excess punishment, members of larger groups will contribute more. Secondly that conducting a real-life experiment with partner treatment and comparing the contributions from another where agents would play the stranger treatment, but knowing as if they were playing partner (to avoid changes in preferences)419, in the second case we will encounter a lower defection. This is a new reason why experiments have found higher contribution in larger groups despite theoretical predictions pointing to the opposite.
3.7.2.2. Group Size Effect on FULL and RING Networks
Let us see how the same phenomenon appears when we implement it in another typical experimental setup. (C) uses a network, where in each sub-group agents can punish exactly one of their fellows, while they also can be punished by only one. (The two of them are different.) This structure is exactly what we have in Contributron as the RING network with SR=1. The most important advantage of this approach for us is that there is no need for compensation in punishment, because in this case the number of contacts and the expected
418 It must be added that although in this case on the long run average all agents face the same amount of punishment, it will not necessarily lead to the same contribution for all network sizes. For agents of small networks the amount of punishment they face will still vary in time more than those in larger groups, which allows the former group to move away from the contribution level of the latter. 419 This is possible, since most of the experiments are conducted through computer interfaces.
- 181 - punishment for all agents are the same, regardless the actual group-size. Basing on our previous experience, it also implies that here a larger group size will not lead to the improvement of contributions. Indeed, the model gives us the following output.
Contribution Contribution with Different Group Sizes Compensated Difference in Contribution Between Treatments with Different Group Sizes Compensated 20 1.2 H L 17.5 H L 2x12 2x12 1 15 3x8 3x8 12.5 0.8 4x6 4x6
10 0.6 6x4 6x4 7.5 8x3 0.4 8x3 5 12 x2 0.2 12 x2 2.5
Period Period 2 4 6 8 10 2 4 6 8 10
Figure 73 – Contributions (left) and difference between partner treatment and the same with reshuffling (right) on RING sub-networks
As expected, there is no difference between the performances of different size networks. Nevertheless, reshuffling still improves contribution, but it does so more or less to the same extent for all sizes. (That is with the reshuffle condition there is no big difference again.)
3.7.2.3. Convergence in Watchfulness
I have emphasized above that most experiments isolate agents from each other except for the information positively revealed, which is strictly controlled by the experimenters. This information includes usually only the contributions made by others. Thus, participants are not informed about the punishment exerted by fellow group members on each other, inhibiting imitation of punishment behavior and possibly distorting real-life behavior. The next question I briefly touch upon is what happens if we allow for average-biased updating in punishment.
ContributionContribution with Different Group Sizes Compensated ContributionContribution with Different Group Sizes Compensated 20 20 17.5 2 x12 17.5 2 x12 H L H L 15 3x8 15 3x8 12.5 4x6 12.5 4x6 10 10 6x4 6x4 7.5 7.5 8x3 8x3 5 5 12 x2 12 x2 2.5 2.5 Period Period 2 4 6 8 10 2 4 6 8 10
Figure 74 – Contributions in a stranger treatment with WUS=0 (left) and WUS=0.13 (right) (WUSC=1)
- 182 - In these experiments I have used WUSC = 1, holding on to that agents cannot see successfulness. Where W was allow to change I have set WUS = 0.13, the same degree of imitative transmission as with BUS (WUS=0 for the control cases.) Note that the difference between these two graphs is not in reshuffling as in the ones before (here both treatments were reshuffled), but in WUS. Below you can check that in the meantime the average W remains constant, and the difference between the contributions of the two cases.
WatchfulnessWatchfulness with Different Group Sizes Compensated Diff . in Contribution Between WUS =0.13 and WUS =0 with Different Group Sizes Cmp 'd 1 H L H L 2 2x12 2x12 0.8
3x8 3x8 1.5
0.6 4x6 4x6
6x4 1 6x4 0.4 8x3 8x3
0.5 0.2 12 x2 12 x2
Period Period 2 4 6 8 10 2 4 6 8 10
Figure 75 – AW (left) and the difference of contributions between the two treatments with WUS=0.13 and WUS=0 (right)
Here we can see again that the difference in the contributions between the different size groups was caused by the different distribution of punishment (between groups and through time): although the average W level remains the same, the converging W levels boost contribution in itself. Also mark that the largest improvement took place in the smallest sub- groups just like in the previous cases, which is quite reasonable for the same reasons given above. Average-biased updating − in addition to larger groups and reshuffling − is the third way of narrowing the distribution of (expected) punishment imposed on the particular agents. It is easy to devise an empirical test for this prediction: experimenters should simply let participants know about how other players punish in their group. (Of course, to avoid retribution, this information should be given without identifying the particular agents.) Finally, it is noteworthy that some studies (e.g. BG on p11) indicate that average punishment per unit of shirking (that is AW in our model) even tends to increase during PG experiments, which suggests that instead of (or in combination with) WUS other means of updating could also be used − a promising direction for future research.
3.7.3. Certainty and Severity of Peer Punishment
The last question we examine is the analogue of the certainty-severity dichotomy discussed in connection with central enforcement. This time, though, we put it into a social context understanding certainty as the willingness of peers to punish, and severity as different PPE and BUDP levels.
3.7.3.1. Mapping Parameter Combinations
- 183 - In principle W, that is certainty as it is seen here, does not only depend on the natural willingness of agents to punish. It measures the effective probability of getting punished by a particular agent, which as hinted before, also involves external factors that influence how easily peer punishment can reach agents. People can be very upset about others’ behavior, but if society does not have the appropriate channels to let potential punishers express themselves towards defectors it will not have a great effect on actual behavior. Similarly, if punishment is delivered, but it is not harsh enough or agents are immune to it, contributions remain low. Different combinations of (effective) certainty and severity will result in different levels of contributions.
0.2 0.4 0.6 0.8 1.
-3. -3.
-2.4 -2.4
15 -1.8 -1.8 10
Contribution 5 E P -3.0 1. P
-2.4 0.8 -1.2 -1.2 -1.8 0.6
PPE -1.2 0.4 W -0.6 -0.6 -0.6 0.2
0.2 0.4 0.6 0.8 1. W
Figure 76 – Mean average contribution with different combinations of W and PPE (Partner treatment, BUDP=−0.23)
The two graphs above represent the same data. On the left we see contributions over a 2D grid, while on the right we can see the same from above with some iso-contribution lines drawn in. We can observe how W and PPE mutually influence each other’s effect on contributions. First we realize that W has an effect even when there is no PPE at all. This is due to BUDP, capturing a phenomenon that has been demonstrated in real-life experiments that punishment can be effective even when it imposes only informal reprimand without any material harm. Observe also that there is a region with PPE > 0 but PPE*W still low420, where contribution remains the same as with PPE=0. The reason is that in this region the optimal B for BUR is still 1, therefore BUR has the same effect at each PPE/W combination. One can see that the effect of W is not linear but concave even in this region. This is easy to understand: on the one hand it is due to the uneven distribution of punishers and defectors some shirkers face more punishment than others which is why they reach a low B already with a moderate W and further increase in W will not have a great effect on their contributions. At the same time a rising W will still affect defectors with less punishers attached to them. On the other hand individual equilibrium points between the effects of BUR and BUND also goes down slower and slower (see equation (3.16)). As a consequence, W has
420 I refer to the product of PPE and W, because the formula for optimal B involves PPE*sum W in the neighborhood of the agent.
- 184 - a decreasing marginal effect on contributions. Naturally, when the certainty of punishment is zero, PPE cannot affect contribution in itself. W and PPE have a strong positive cross-effect, each of them strengthening the other’s influence over a large area. (Remember that according to experimental studies even though informal punishment is effective, combining it with material penalty had a significantly stronger influence on contributions.) Besides, note that we find the highest contributions when both certainty and severity is high. With Contributron it is equally easy to get the contribution level for combinations of W with BUDP at a constant PPE, and PPE and BUDP with a constant W.421
0.2 0.4 0.6 0.8 1. -0.2 -0.4 -0.6 -0.8 -1.
-0.3 -0.3 -0.3 -0.3
-0.24 -0.24 -0.24 -0.24
-0.18 -0.18 -0.18 -0.18 P P D D U U B B
-0.12 -0.12 -0.12 -0.12
-0.06 -0.06 -0.06 -0.06
0.2 0.4 0.6 0.8 1. -0.2 -0.4 -0.6 -0.8 -1. W PPE
Figure 77 – Contributions with different combinations of BUDP / W (PPE=−2.06) and BUDP / PPE (W=0.75 for the punisher types) with a heterogeneous simulated population
Considering what already has been said, there is nothing very surprising in these graphs, although there are a couple of things to mention. In the left picture we again see the concave effect of W at all BUDP levels. Nevertheless, here we do not have the area with parallel contour lines as with PPE: BUDP affects contributions at all levels. On the right we again find that until a certain point PPE has no effect at all, plus that BUDP has a similarly concave effect as W above, both for the same reason as before. We again find the highest contributions when both parameters are high. On both maps we find cross-effects: BUDP supports W, although the other way around this is not so clear: some W is of course needed for BUDP to have an effect at all, but since here we do not have a threshold for BUDP to become effective (like above the area where PPE had no influence), and because at this PPE level W has a strong effect in itself this cross effect is not so spectacular. On the right, we see negative cross-effects: with a higher BUDP PPE affects contribution levels less and vice versa. It is quite natural − when one motivation already suppresses defection, adding another can suppress it less. A trivial conclusion: the primary objective is to create informal channels through which punishers can express themselves (which activates the reaction to informal
421 Of course we could run simulations on all three dimensions; the difficulty arises only when we try to present the results in two dimensions.
- 185 - punishment), enhancing possibilities to turn this into material disadvantage should follow afterwards.
3.7.3.2. Finding the Optimal Mix
This is just one last remark to the above figures. It is quite clear that we can achieve maximal contribution by pushing up both certainty and severity. But supposing we have some kind of trade-off between them (PPE, BUDP and W), the simulated topologies make it possible to find the optimal mix of the quantities in question. This trade-off needs not to be a monetary one: for instance agents may have a constant capacity (time, energy, attention) which they can use in two ways: punishing detected defectors more harshly (to increase PPE) or checking and punishing more defectors (to increase W). If we have a (not necessarily linear) function for the rate of transformation between the two uses, we can draw the feasible combinations into the above map and find where it touches contour lines to obtain the optimal level of W and PPE that maximizes contribution, as demonstrated below.
0.2 0.4 0.6 0.8 1.
-3. -3.
-2.4 -2.4
-1.8 -1.8 E P P
-1.2 -1.2
-0.6 -0.6
0.2 0.4 0.6 0.8 1. W
Figure 78 – Finding the optimal combination of severity and certainty
3.7.4. Summary of Findings
In this chapter we have obtained the following results:
● Parameters of Contributron can be calibrated using data from real-life experiments. The model output is close to experimental findings.
● Larger groups tend to contribute more even if we compensate for the higher punishment caused by the larger number of neighbors, because defectors face more even (cross-section) punishment. Whether group size affects
- 186 - contributions depends upon the internal structure of these groups: on a RING network we do not find difference between them.
● Reshuffling increases contribution by distributing punishment capacity more equally in time. By introducing reshuffling the highest growth in contributions is attained in the smallest groups.
● Allowing for average-biased transmission of punishment behavior raises contributions even if the average willingness to punish is constant, because of the convergence of expected punishment defectors face.
● Different combinations of severity and certainty of peer punishment lead to different levels of average contributions. Certainty (W) and severity (PPE, BUDP) usually have a positive cross-effect on contribution, while different measures of severity (PPE and BUDP) a negative one. We find concavity in contributions with both certainty and severity.
● Simulated contribution levels facilitate obtaining optimal combinations of certainty and severity provided there is a trade-off between them.
As usual by now, I must add that the topics investigated in this chapter constitute only a tiny fraction of what the model is capable of, leaving ample space for future projects.
- 187 - 4.Part IV
Conclusion and Further Development
- 188 - In part three we have obtained numerous results. I certainly do not intend to repeat all of them here; but as a conclusion, I would like to collect the most important findings and achievements, putting them together thematically. First I am going to list the phenomena produced by the model that supports its validity, second I gather the most interesting achievements and findings we came across, then I will give some recommendations for further research using the model and finally deliver a few ideas concerning agent behavior, the representation of social networks and some others by which the model could be extended in the future to capture even more phenomena.
4.1. Validity
Contributron has demonstrated that it is capable to reproduce a range of theoretical results and empirical findings as well. Which of them we obtained, depended our assumptions on agent behavior and network structure, the corresponding choice of parameters and other settings fed into the model. Starting off with rational agents we have got the optima predicted by analytical maximization. With this simple setup, we have also managed to replicate the results of economics of crime proposing severe punishments and an optimal level of certainty. Introducing heterogeneity into the population let us observe hump-shaped contribution patterns or Laffer-curves familiar from macro-economics. Accepting peer penalty and variable norm adherence we could synthesize norm cascades resulting in long periods of stability separated by rapid shifts in contribution. Estimating parameters from empirical studies we managed to match simulation output with experimental results. All these results establish Contributron as a valid tool of simulation study.
4.2. Achivements
First of all, the achievement underpinning all the rest is that combining the most general principles collected from the literature we have managed to create a both theoretically and empirically valid experimental tool. Contributron is flexible and versatile; the results listed below represent only a tiny fraction that the model is capable of. In addition, I think that the implementation of the model has also succeeded to demonstrate the advantages of a new and efficient programming technique for social simulation, namely linking Mathematica as a front end to a separate simulation executable written in C++. In addition it must be emphasized that the Mathematica front-end could easily be adapted to completely different projects, and used as a stand-alone product. Agents in the model are able to update their strategies represented by Boldness and Watchfulness. This on the population level leads to evolution: Contributron is an evolutionary model. We have demonstrated that payoff-biased imitation is able to marshal a population to the optimal strategy without any of the agents maximizing individually. This process, however, requires favorable circumstances, and we have identified some key elements that determine whether evolution can succeed, involving high certainty of punishment, sufficiently long term memory and an appropriate level of variability422 in the population. We have also
422 The most important prerequisite of evolution is variability. For social evolution the primary form of variability is variability of behavior, in our model governed by Boldness and Watchfulness. However, there is a secondary, underlying form of variability, variablity of personality that has only an indirect effect on evolution through influencing the primary determinants of behavior. Real societies consist of different people, who not
- 189 - recognized some connections between the evolutionary process and individual maximization. First we have shown that one of the central elements of our modeled evolution, weighed updating can be perceived as a special form of maximization. Second we have realized that evolution always builds upon ex post outcomes whereby maximization takes into consideration ex ante expected values. This in turn, in a stochastic environment − which essentially our real world is − can easily make a difference between the outcome of rational maximization and the evolutional result of selective imitation. Our findings also call attention to that what so far has been taken as a evidence of individual maximization might be only the outcome of a blind evolutionary process, where the more successful is selected for. Evolution is also largely influenced by the rules of interaction, one of whose most important elements in social evolution is social networks. Having explored analytically their connectivity, we have seen numerous examples for the experimental realization of its consequences. We have seen how small-world links can speed up convergence. We have also learnt about the relevance of changing network structure and found out how network regularity and symmetry can influence the efficiency of peer punishment. Imitation as the most characteristic component of evolution largely amplified the role of network structure, while agent and network heterogeneity illustrated the importance of the spatial and parametrical distribution of different agent types as opposed to mean field models and representative agents. We have found that large groups, reshuffled agent pools and those where imitation of punishment behavior was possible contributed more, and proposed empirical tests for checking these hypotheses. Some of our experiments warned that seemingly irrelevant differences in network structure may result in fundamental alterations in output. Our experiments also added to the long-standing debate on the certainty and severity of punishment. Firstly, we have found that a low certainty central punishment scheme can hinder the attainment of optimal defection level with payoff-biased imitators and discounted reputation, allowing agents to take example from those who are successful the most often. Secondly, we have demonstrated how this new tool can be used to find the optimal certainty levels in more involved situations when analytical methods are not appropriate. Finally, we have learnt probably the most instructive lesson in connection with policy making. By relaxing the stringent initial assumptions on agents and letting central and local enforcement interact we found that central policies, especially raising severity without paying due attention to its effect on localized enforcement can easily backfire.
In addition, I think Part III successfully met all objectives set out at the beginning.
4.3. Further Research
On several occasions, following the introduction of basic cases we have usually advanced a few steps further into the new domain opened up by Contributron. At many places having started off with a simple community, usually taking maximizers and homogeneous populations as the basic case, we continued by looking at how other kinds of agents would behave in similar situations or how different arrangements of agents influence the results. Heterogeneous populations and network variations have revealed a vast unexplored space of
only behave but also think differently. Personality in Contributron is captured by the various updating parameters that can be set differently for each individual, allowing for the composition of complex societies.
- 190 - deeply entangled communities into which we have only launched a few small probes yet. Furthermore, norm cascades directed us towards exploring joint oscillatory dynamics of the two norms represented in our model, the most fundamental cases of policy issues unlocked a wide range of opportunities so far beyond the horizons of formal investigation and combining the power of experimental economics and social simulations has barely been touched upon considering the possibilities still left to be discovered. All these areas can be further investigated using the model even in its present form. Here are some more concrete propositions:
● We have seen that payoff-biased imitative transmission can lead to the community-wide emergence of the payoff-maximizing defection level. We have also seen that whether and how fast it happens depend upon our assumptions on the society. It would be interesting to see a survey on this issue taking forward the current findings, considering more settings and parameter combinations.
● One broad question that the model is capable to handle but it was impossible to go into its details here is checking the effect of mixing up different agent types to different degree. One could use either the Swapping shuffle type or the CUSTOM_RANDOMIZE network type to investigate this issue.
● It would be interesting to see a more detailed investigation of the conditions for norm cascades. For example it would be not very hard to set up experiments to check how often they occur in different situations, how they can be best prevented when they are undesirable and how to support them in the opposite case.
● Contributron has a number of built-in network types, whose properties have been investigated in this work to a certain extent. There are, though, many other kinds of networks in the literature, whose behavior could be explored and compared with the present findings.
● Recalling one of the ideas given at the end of the policy chapter, Contributron could be used to seek policies aiming at societal questions instead of simply maximizing contribution. One such departure could be for instance to minimize the gap between the welfare of high and low income groups with a constraint on minimal contribution.
● Although we have managed to calibrate our model to experimental data from the literature, it would be useful to carry out real-world experiments firstly to gather data directly for the calibration of Contributron, and secondly to check the hypotheses set up with it.
4.4. Future Development
In addition to what is already possible to do with the model, there are also numerous ways for extending it.
- 191 - 4.4.1. Agent Properties
● Rational updating could be made more realistic. Agents in Contributron have perfect information, which is close to classical economic theory but in most cases quite far from reality. This could be modified for example to give agents noisy information, or suppose that they are only capable to dynamically update their knowledge of the environment based on their experience. Calculating the optimum from the data could be also made less perfect.
● Instead of looking at people as being permanently changed by their environment, one can suppose that they are only diverted temporally and tend to revert to the behavior determined by their inherent personality when external effects cease to affect them. This could be incorporated by a mechanism that would pull Boldness and Watchfulness towards their initial conditions.
● Some experimental papers suggest that in Public Good situations punishment depends on the relative deviation of contribution from a group average rather that an absolute measure of it. This would be easy to implement in our model. Another way of modifying this bit in the continuous contribution case is making the probability of getting caught if checked some other function of Boldness instead of simply equating with it. One candidate is to control the shape of this function similarly to how BUSC and WUSC work. (In Contributron the probability of getting caught if checked is simply equal to Boldness in the continuous case as well, to be consistent with the discrete situation, where it is reasonable to suppose that punishment arrives only after having shirked.)
● Another extension of punishment behavior could be introducing other motives to punish. The reader probably remembers that there is a minority of players who punish cooperators, which gives background for inserting spitefulness in the model. Besides, strategic punishment is a further option. This, although a straightforward application of classical economic principles, does not find too much endorsement in empirical studies. (This is the cause why it has been left out originally.) Strategic agents could possibly compare the cost of punishment and the expected growth in their income due to it.
● Agents could learn by example, raising their contributions already when seeing other agents getting punished, without themselves being caught first. (In fact, indirectly it is already in the model through the direct effect in W and self- punishment.) One way to do this would be to introduce a new parameter to determine the strength of this new kind of direct effect relative to the old BUDP and BUDC.
● The updating parameters of agents could also be made variable during runs. The more basic approach is to introduce mutation. It could be interpreted for example as migration, which is quite common in real communities. (In fact there is a mechanism of migration already in the model: isolated sub-groups with reshuffling, which we have used in the chapter of experimental connection.) Another related idea is using some kind of genetic algorithm,
- 192 - which would update the agent pool regularly, basing on the relative successfulness of the different types. (Many analytical models use a similar but simpler idea, replicator dynamics.)
● The endowment could be endogeneized. This could be done similarly to the way public good games operate with it: multiplying the total contribution with a constant and paying it back to the agents. Though a uniform change in the endowment for all agents would not alter the order of reputation in the population (thus imitative transmission would not be affected by it), it could still have an influence through the rational updating.
4.4.2. Network Extensions
● Although Contributron is able to handle any (discrete) network setup through the CUSTOM type, building in the parametric generation of further network types into the executable would greatly facilitate their exploration.
● Another possibility is to upgrade the model to handle different strength connections. (This could influence the severity and certainty of peer punishment or the quality of information transmitted through that link. It also could be used to make a difference between the surveillance undertaken by the central authority and the peers.)
● Related to the previous point the strength of the connections could be made dynamic. For example it is reasonable to assume that when someone is found to shirk, it could induce the inspector to look with a higher probability next time at that agent.
4.4.3. Miscellaneous Improvements
● The most schematic element of the present model is the central authority. A promising direction of extension is to use the possibilities of simulation more intensively in this respect too, and let the central authority employ more complicated policy rules for example by implementing conditional tax inspection or dynamical rules of policing.
● We have already mentioned that at least in public good games peer punishment may be conditioned on a relative measure of contribution rather than an absolute one. This illustrates that in different manifestations of the contribution-punishment problem particular elements of the model might operate slightly differently. While keeping the main skeleton and functionality of the model intact certain parts could easily be fashioned to these specific variants of the same general problem.
● Thanks to the versatility of Mathematica, it is already possible to automate the manipulation of the ini file. Nevertheless, a special tool could be developed to aid the experimenter editing it without being compelled to get to much involved in programming.
- 193 - I would like to close this work with a subjective remark. Throughout designing and building Contributron I laid an emphasis on keeping it as clear and transparent as possible. I understand that at first sight it probably looks much more complicated than what the reader is used to, but getting a second look one can realize that all mechanisms featured in the model are very basic. And still, knowing all bits of the underlying rules, sometimes it took me long hours to figure out how this simple system could generate the intricate output I was staring at. What it taught me is a bit of humility towards complexity and tact, especially indispensable when one turns from a man made gadget to the whole wide world.
- 194 -
5.Appendix 1 – Parameter Arrangements and Abbreviations CB1 – Control Bits #1 CB2 – Control Bits #2 G − Generations P − Population XTRA1 XTRA2 SR − Sight Range SEED CB1 CB2 (int) (double) E − Endowment TR − Tax Rate RA − Reputation Attenuation G STEP RUNS P SR CPR − Central Probability CPE − Central Penalty PPE − Peer Penalty E TR RA PC − Peer Cost BUR − Boldness Update Rational CPR CPE PPE PC BUDC − Boldness Update Direct Central BUDP − Boldness Update Direct Peer BUS − Boldness Update Social BUR BUDC BUDP BUS BUSC BUSC − Boldness Update Social Curvature BUND − Boldness Update Noise Deviation BUNM − Boldness Update Noise Mean BUND BUNM WUR − Watchfulness Update Rational WUDC − Watchfulness Update Direct Central WUDP − Watchfulness Update Direct Peer WUR WUDC WUDP WUS WUSC WUS − Watchfulness Update Social WUSC − Watchfulness Update Social Curvature WUND − Watchfulness Update Noise Deviation WUND WUNM0 WUNM1 WMIN WMAX WUNM0 − Watchfulness Update Noise Mean (B=0) WUNM1 − Watchfulness Update Noise Mean (B=1) WMIN − Watchfulness Minimum Arrangement of Parameters in Mathematica Function Contributron[] WMAX − Watchfulness Maximum
Abbreviation of Parameter Names Control Bits in CB1 (CB_DEs)
Averaged Data Export
#0 − Boldness #1 − Reputation #2 − Watchfulness #3 − Contribution #4 − Central Checks #5 − Peer Checks #6 − Central Punishment Received #7 − Peer Punishment Received #8 − Peer Punishment Inflicted
Individual Data Export
#16 − Boldness #17 − Reputation #18 − Watchfulness #19 − Contribution #20 − Central Checks #21 − Peer Checks #22 − Central Punishment Received #23 − Peer Punishment Received #24 − Peer Punishment Inflicted
Control Bits in CB2
#0 − CB_CC (Continuous Contribution) #4 − CB_SN (Symmetric Network) #8 − CB_SP (Self-Punishment) #9 − CB_PPEP (PPE is Penalty) #12 − CB_WUDS (Watchfulness Update Direct Self) #16 − CB_AE (Averaged Export) #20 − CB_EN (Export Network) #24 − CB_EVA (Export Variance for Averaged) #25 − CB_EVI (Export Variance for Individual)
Variable Abbreviations
B − Boldness R − Reputation W − Watchfulness
Network Abbreviations
RCOR − Random Constant Regular RCOP − Random Constant Probabilistic RCHR − Random Changing Regular RCHP − Random Changing Probabilistic Appendix 2 – Flowchart of Contributron.exe
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