Agent-Based Models in Sociology Federico Bianchi∗ and Flaminio Squazzoni

Advanced Review

Agent-based models in sociology Federico Bianchi∗ and Flaminio Squazzoni

This article looks at 20 years of applications of agent-based models (ABMs) in sociology and, in particular, their explanatory achievements and methodological insights. These applications have helped sociologists to examine agent interaction in social outcomes and have helped shift analyses away from structural and aggregate factors, to the role of agency. They have improved the realism of the micro-behavioral foundations of sociological models, by complementing analytic modeling and game theory–inspired analyses. Secondly, they have helped us to dissect the role of social structures in constraining individual behavior more precisely than in variable-based sociology. Finally, simulation outcomes have given us a more dynamic view of the interplay between individual behavior and social structures, thus promoting a more evolutionary and process-based approach to social facts. Attention here has been paid to social norms, social inﬂuence, and culture dynamics, across different disciplines such as behavioral sciences, complexity science, sociology, and economics. We argue that these applications can help sociology to achieve more rigorous research standards, by promoting a modeling environment and providing tighter cross-disciplinary integration. Recently, certain methodological improvements toward model standardization, replication, and validation have been achieved. As a result, the impact of these models in sociology is expected to grow even more in the future. © 2015 Wiley Periodicals, Inc.

Howtocitethisarticle: WIREs Comput Stat 2015, 7:284–306. doi: 10.1002/wics.1356

Keywords: agent-based models; sociology; social norms; social inﬂuence; collective behavior; social networks

INTRODUCTION time series of aggregate data or certain stylized facts.3,4 gent-based models (ABMs) are computer simula- The origins of ABMs in sociology can be traced tions of social interaction between heterogeneous A back to the pioneering contributions by James S. Cole- agents (e.g., individuals, firms, or states), embed- 5–7 dedinsocialstructures(e.g.,socialnetworks,spa- man and Raymond Boudon in the 1960s and the tial neighborhoods, or institutional scaffolds). These publication of the first two volumes of The Journal are built to observe and analyze the emergence of of Mathematical Sociology in 1971. These included aggregate outcomes.1,2 By manipulating behavioral two important articles by James M. Sakoda and 8,9 or interaction model parameters, whether guided Thomas C. Schelling on segregation dynamics. In by empirical evidence or theory, micro-generative these contributions, studying social outcomes by mod- mechanisms can be explored that can account for eling agent behavior and interaction in a computer macro-scale system behavior, that is, an existing was considered an alternative to the functionalistic, hyper-theoretical, macro-oriented social system theo- ∗Correspondence to: [email protected] ries that dominated sociology at that time. Department of Economics and Management, University of Brescia, However, it was only from the 1990s that ABM Brescia, Italy applications reached a critical mass. This develop- Conflict of interest: The authors have declared no conflicts of interest ment was due to the increasing computing power and for this article. the diffusion of the first open source ABM platforms.

These platforms made explicit individual behavior behavior, the subtle nuances of individual rationality, models possible for the first time, without requiring and the influence of social contexts in understanding excessive computing skills by the modeler. Initial soci- aggregate behavior. They also showed that sociolog- ological applications in the late 1990s covered the fol- ical relevance increases when the interplay between lowing areas: cooperation and social norms, diffusion, individual behavior and social networks is looked at social influence, culture dynamics, residential ethnic in a more dynamic, coevolutionary way. segregation, political coalitions, and collective opin- The third paragraph looks at examples of ABMs, ions, to name but a few.10–14 which investigated social influence mechanisms and All these applications demonstrated that com- the influence of certain structural constraints on social putational models can look at the dynamic nature outcomes, such as residential segregation, stratifica- of social facts better than most other social scientific tion, and collective opinions. These examples help us methods. These include analytical equation–based to understand that certain facets of the social structure models, used in standard economics and game theory; might influence social connections among individuals. statistical regression models, used in macro-sociology; As a result, they may have wider implications, includ- and un-formalized, descriptive accounts, used in ing not only pressure toward social uniformity and qualitative sociology. Due to mathematical restric- convergence but also persistence of diversity in cul- tions, standard game theory and analytical modeling ture, norms, or attitudes. At the same time, they help cannot account for the irreducible heterogeneity of us to conceive the constructive role of the interplay of social behavior or look at out-of-equilibrium social behavioral mechanisms and social structures in under- dynamics, both of which are intrinsic to the ABM standing the emergence of collective phenomena. approach. In this sense, the ABM approach is closer Finally, in the conclusion, we summarize the key to behavioral game theory, which studies a variety findings and discuss the methodological implications. of preferences and motivations through experiments, rather than standard rational choice theory, where homogeneous individual selfishness is assumed. While COOPERATION AND SOCIAL NORMS variable-based statistical models cannot easily deal Social life is rich with complex forms of cooper- with micro-generative processes, which are key to ation between unrelated individuals that are chan- ABMs, descriptive, qualitative accounts cannot dis- neled through social norms and institutions. Donating entangle the effects of social networks and at the blood, being a witness at a trial, or reviewing an arti- same time look at space, time, and large-scale social cle for a journal would not be possible if we were processes in the same way as ABMs can. not able to overcome the temptation of self-interest By reviewing the first wave of ABMs in sociol- to benefit others with our own effort. Given that natu- ogy in the 1990s, Macy and Willer15 emphasized that ral and social selection tend to encourage competition, ABMs are instrumental when the macro patterns of social norms and institutions must exist to provide sociological interest are not the simple aggregation of a context for cooperation. Understanding in which individual attributes but the result of bottom-up pro- contexts and for what reasons individuals can col- cesses at a relational level. Time has progressed since lectively generate social welfare despite self-interest this influential review and advances have been made is one of the most important missions of social both in the extent and scope of ABM applications, in science. the number of sociological publications, and in their We will look at the importance of certain social methodological rigor. This article aims to report on mechanisms in promoting cooperation in hostile envi- these recent advances by considering examples, which ronments, where there is a conflict between individual looked at the importance of behavioral factors, cases self-interest and group outcomes. Examples of these that tested the effect of structural factors, and mod- mechanisms could be direct and indirect reciprocity, els that pointed to the dynamic interplay of individual reputation, social punishment, trust, and social behavior and social structures. conventions. In this field, fruitful cross-fertilization The article is organized as follows. The fol- already exists between behavioral game theory and lowing paragraph looks at ABMs, which investigated ABM sociological analysis of social norms, with social norms in cooperation and competition pro- interesting extensions and modifications of stan- cesses among individuals in stylized interaction con- dard game theory. Here, simulations were used to texts. This is one of the most vibrant ABM fields, complement problems of analytic tractability of where sociology and behavioral game theory have use- standard game theory as well as for exploring depar- fully interacted.16 Their results showed the importance tures from its deductive, equilibrium-dominated of considering the fundamental heterogeneity of social framework.

Direct Reciprocity here is that group identity or tags could substitute or A key mechanism of social life is reciprocity, i.e., a magnify direct reciprocity. form of conditional cooperation between related or Hales24 built an evolutionary model that showed unrelated individuals, which can be either direct or that cooperation could emerge in a mixed popula- indirect.17 Direct reciprocity means that two individ- tion of cooperators and defectors with randomly dis- uals are expected to cooperate if the probability of tributed tags playing one-shot Prisoner’s Dilemma their future encounter exceeds the cost/benefit ratio games with in-group members. Results showed that of the altruistic act at an individual level. In this case, the formation of same-tag local clusters, in which it is likely that certain aspects of social structure can cooperative groups eventually outperformed nonco- have significant implications for cooperation as they operative ones, could work even without assuming the influence the probability of encounters between two memory of past experience, nor reciprocity-oriented , individuals, and so the type of behavior they are strategies. Hammond and Axelrod25 26 modeled a exposed to.18 population of agents with different tags who could It is widely acknowledged that the embeddedness decide whether to cooperate or defect with in-group of agents in a spatial structure dramatically increases and out-group agents. Without building in-group cooperation, as this determines a higher probability favoritism in the model, simulations showed that of encounter between correlated agents.19 An interest- the evolution of cooperation in a spatial structure ing problem is to understand whether this can also could be sustained by the emergence of a domi- happen in non-spatially related structures. A good nant ‘ethnocentric’ strategy, that is, by which agents ABM example of this is a study by Cohen, Riolo, and cooperated with in-group members and defected with Axelrod on an iterated Prisoner’s Dilemma20 (see also outsiders, through the formation of local clusters of Nowak and Sigmund21). They simulated a popula- same-tag agents. Recently, Bausch27 has questioned tion of agents, who could cooperate or defect, recipro- the tag-driven nature of the results of Hammond and cate their opponent’s behavior (i.e., cooperating with Axelrod, arguing that higher levels of cooperation cooperators and defecting with defectors), and imi- might even be obtained by simply constraining interac- tate the behavior of the highest fitted individual they tion and reproduction to occur locally, without mod- encountered (with some noise), thus learning behav- eling different tags and preferential cooperation. ioral strategies from the social environment. They While these examples examined the importance manipulated the initial network topology that con- of forward-looking strategies in repeated dyadic nected agents to each other, by testing random encoun- interaction, cooperation may also emerge from ters, spatial neighborhoods, small-world networks, backward-looking strategies, with individuals capable and fixed networks. Results showed that even the of learning from past experience and adjusting their sole persistence of interaction patterns from initially behavior dynamically. Building on previous work on random encounters could make cooperation possible stochastic learning algorithms,28 Macy and Flache29 between selfish agents as it preserves favorable condi- built a series of models that included a variety of tions for direct reciprocity, e.g., cooperators interact- two-person cooperation dilemmas. Their results ing more frequently among each other and receiving showed that adapting backward-looking agents could higher payoffs. This situation did not vary when agent generate a self-reinforcing cooperative equilibrium behavior was spatially correlated, i.e., spatial effects but only within a narrow range of intermediate levels existed between neighboring agents (see also Axelrod of the agents’ aspiration. Mutual defection was more et al.22). likely if agents had low or high aspiration levels as in Although important, these examples neither these cases the context made defection worthwhile, assume a considerable influence of the social struc- due to agent inertia (low aspiration) or individual ture in shaping individual behavior nor look at the dissatisfaction (high aspiration). social mechanisms that exist to help individuals pre- The situation can change if agents could exploit dict other agents’ behavior. If we consider that our forms of interpersonal commitment against the life is mostly structured into social groups, it is prob- risk of being cheated. In this respect, following able that cooperation is influenced by group identity, experimental research about commitment in dyadic so that we prefer to cooperate with in-group members exchange, Back and Flache30 looked at the viability and are less fair with outsiders. Coherently, in many of committing—i.e., acting unconditionally coopera- circumstances, we tend to use tags or etiquettes (e.g., tively with some partners who have previously proved color of skin, group dress style, or any other obser- to be reliable—against a wide spectrum of other vational trait) to predict behavior,23 which can even exchange strategies in a competitive environment. make us unconscious victims of stereotypes. The point Results showed that commitment-based strategies

TABLE 1 The Impact of Referee Behavior on the Quality and allocates resources inefficiently (see Table 1; see also Efﬁciency of Peer Review in Various Selective Environments (Ref 31, Thurner and Hanel32; Squazzoni and Gandelli33). p. 4.3) Evaluation Resource Reviewing Scenario Bias (%) Loss (%) Expenses (%) Indirect Reciprocity and Reputation It is worth noting that individuals can also cooperate 75% of published submissions indirectly via third parties. In these cases, individu- No reciprocity 14.10 5.69 23.47 als could expect future benefits by cooperating with Indirect reciprocity 12.58 6.51 44.16 a counterpart from other partners, e.g., other group Fairness 13.14 7.48 40.61 members, or by accessing or being subject to repu- 50% of published submissions tational information, e.g., cooperating with someone No reciprocity 26.32 15.65 30.32 establishes good reputation that will be awarded by others.34 Indirect reciprocity 25.32 12.64 39.88 Behavioral and evolutionary research has Fairness 15.68 8.60 38.68 recently shown that the complex cooperation scaffolds 25% of published submissions that characterize social life seem to primarily depend No reciprocity 28.00 15.01 29.47 on these complex forms of indirect reciprocity.17 This Indirect reciprocity 43.12 16.92 33.39 has interesting sociological implications as social Fairness 19.52 8.32 38.29 relationships pass from a dyadic to a triadic form and network effects are also included. This can help In ‘No reciprocity’, the reliability of scientists as referees was random. In us to understand why social evolution involves the ‘Indirect reciprocity’, referees were reliable if they had published as authors in the previous round, otherwise they reciprocated rejection by being unreliable. establishment of generalized forms of social exchange In ‘Fairness’, referees were reliable if they had received pertinent evaluations and large groups of unrelated individuals beyond when authors in the previous round, whether they had been published or not. The opposite was true in case of impertinent evaluation. Evaluation direct reciprocity motives. bias measured the number of low quality articles that were published when In this respect, many ABM studies have looked they did not deserve to be. Resource loss measured the average number of resources at the system level that were wasted because of unpublished authors, at the impact of reputation as a form of indirect who deserved to be published, compared with the optimal solution, i.e., reciprocity.35,36 These studies emphasized two impor- when only the best authors were published. Reviewing expenses measured the percentage of resources spent by agents for reviewing compared with the tant functions of reputation: learning (accessing infor- resources invested by submitting authors. mation about unknown partners via third parties, which was not previously available and/or was too , are more viable than even tolerant versions of direct costly) and social control37 38 (monitoring and pun- reciprocity, as they allow agents to create wider and ishing norm violators through socially shared reputa- more efficient exchange networks, while avoiding tional signals). the vicious cycle of ‘keeping the books balanced’, As regards to learning, Boero et al.39 developed which makes reciprocity-based strategies vulnerable an ABM calibrated on behavioral data gathered from to cascades of mutual retaliatory defection. a laboratory experiment where subjects were asked to It is worth noting that recent ABM studies have take investment decisions in a simulated financial mar- analyzed the impact of reciprocity also in peer review ket characterized by asymmetries of information and and found a possible negative side of reciprocity when uncertainty. Subjects had different investment options, social sanctioning is absent or weak. Squazzoni and which were more or less risky and could receive/send Gandelli31 modeled the strategic behavior of referees information by/to others, so mimicking the formation in a population of scientists called on to act as authors and circulation of reputational information. Results and referees during the peer-review process in differ- showed, firstly, that subjects followed three types ent competitive publication environments. Scenarios of behavior, coherent with behavioral game theory where referees were randomly reliable (i.e., providing findings, i.e., always cooperating with others by more or less pertinent evaluation of author submis- sharing reliable information, reciprocating reliable sions’ quality) were compared with others in which information only with reliable partners, and cheating referees could strategically reciprocate past experi- by always providing unreliable information to others. ence as authors by being more or less reliable with Secondly, results showed that socially sharing reputa- new authors. Their simulations showed that if ref- tional information was beneficial for the exploration erees’ reciprocity is not inspired by fairness (con- capabilities of agents in situations of uncertainty, tributing to scientific progress as a public good), but independent of the quality of the information shared. only by past publication or rejection when authors, Finally, they showed that reputation (social sharing peer review generates dramatic publication bias and of personal evaluation, even if potentially biased) was

Volume 7, July/August 2015 © 2015 Wiley Periodicals, Inc. 287 Advanced Review wires.wiley.com/compstats more effective than personal experience (formation of 100 an opinion on the counterpart in direct interaction) in 90 detecting reliable information partners and reducing 80 the amount of false reputational information in the 70 system. 60 With regard to social control, Conte and Selfish 50 Paolucci40 developed a model that also distinguished Percent 40 ‘image’ from ‘reputation’ and focused on social pro- Reciprocator 30 cesses of reputation formation and transmission. Cooperator 20 They simulated a population of agents that followed Shirking rate heterogeneous behavior, i.e., self-interest, altruism, 10 and norm compliance, in a social dilemma situa- 0 tion and manipulated simulation scenarios to add 0 500 1000 1500 2000 2500 3000 socially shared evaluation of other agents’ behavior. Period Results showed that by allowing individuals to share FIGURE 1| Coexistence of behaviors and shirking rate in a typical the social cost of sanctioning against self-interested simulation run (Reprinted with permission from Ref 45, p. 21 Copyright behavior, reputation provided room for evolutionary 2004 Elsevier Ltd). stability of cooperation at levels hardly achievable by other mechanisms, e.g., direct reciprocity or cog- reciprocators were functional in keeping the level of nitively sophisticated trustful partners’ detection. cheating under control in each group (see the shirking Furthermore, they found that the circulation of false rate as a measure of resources lost by the group due to bad reputation tended to protect normative behavior cheating in Figure 1). This was due to the fact that the more than leniency (false good reputation) or silence. higher the number of cooperators in a group without This work has influenced a large body of ABM reciprocators, the higher the chance that the group dis- research on reputation as a social control device for banded due to high payoffs for shirking. This means 41–43 group behavior. that group structure may be the key to evolutionary social selection, even more than individual strategies (see also the test on the case of team collaboration in Social Punishment organizations by Carpenter et al.46). This is a relevant Another form of indirect reciprocity is social pun- finding as it paves the way to consider whether social ishment. Indeed, while reciprocating bad behavior selection can be multilevel, working not only at a with a bad behavior in some circumstances can cre- genetic-individual level but also at a social group level. ate the conditions for cooperation, social life is full These findings were extended by Boyd et al.47 to of examples of individuals bearing a personal cost situations of public punishment (i.e., the establishment for punishing wrongdoers, e.g., an individual report- of an institution, which monitors people’s behavior ing misbehavior to the police to benefit a victim. This and punishes wrongdoers by exploiting economies of behavior is called ‘strong reciprocity’ as it implies a scale). Their results showed that in the case of insti- direct reduction of payoffs imposed on the cheater at tutional punishment also, the presence of a minimal the expenses of the punisher without direct reciprocal fraction of strong reciprocators intrinsically motivated benefits for the latter.44 by social norms to support institutional punishment Empirically inspired by the case of mobile by paying fees and help social monitoring is instru- hunter-gatherer groups in the Late Pleistocene, Bowles mental to maintain cooperation over time. and Gintis45 have developed an ABM where a popula- More recently, Andrighetto et al.48 built an inter- tion of agents played an n-player Prisoner’s Dilemma esting ABM based on experimental data in a pub- that mimicked cooperation problems in hunting, food lic goods game similar to the previous examples, gathering, and common defense without any central- where punishment was combined with normative sig- ized institution. They explored a mixed population of naling. In this case, agents were called on to decide egoists, cooperators, and strong reciprocators. Due to whether to cooperate by contributing to the public the presence of self-interested agents, group benefits good or defect by exploiting other agents’ contri- could be eroded by the fact that certain individuals bution, punishing defectors, and sending signals to could exploit the collaborative work of others without others about the appropriate amount of contribution themselves contributing. They found that the robust- expected (i.e., the norm). As it is a focal point for ness of cooperation depended on the coexistence what others expect as an appropriate contribution, of these behaviors at a group level and that strong signaling could affect individual preferences. Their

288 © 2015 Wiley Periodicals, Inc. Volume 7, July/August 2015 WIREs Computational Statistics Agent-based models in sociology simulations showed that punishment accompanied by population of learning agents. These played a repeated norm signaling can ensure more robust cooperation version of the Prisoner’s Dilemma with an exit option at a lower cost for the group than when acting alone. and the possibility to choose to play with a neighbor or They also showed that punishment is more effective a stranger with different opportunity and transaction when norm communication has already proved to be costs. Simulations found a curvilinear effect of mobil- important for the perception of the norm by individu- ity on trust. Indeed, the ability to detect trustwor- als. This socio-cognitive approach has been followed thy partners emerged only beyond moderate levels of by other ABM studies to examine the cognitive coun- mobility, which allowed agents to meet other partners. terpart of social norms and the importance of social In case of higher levels of mobility, trust decreased contexts. These provide normative meaning and sig- because agents could not appropriately discriminate nals for individuals in typical social dilemmas, using trust anymore. an interesting mix of ABM, experimental and qualita- These studies indicate that one of the main tive methods.49–52 challenges for cooperation in trust situations is the capability of agents to detect trustworthy partners and build stable forms of interaction around them. Trust In this respect, some studies have looked at partner , In many cases, we provide relevant information, time, selection in dynamic networks.58 59 Theideahereis or money to others when we trust that they will honor that not only might individual behavior vary from our help. However, in competitive environments and person to person and within the same person over in situations of information asymmetry, distrust could time, but social networks are also constantly changing. prevail given that the potential benefit of interacting This reflects new opportunities or constraints for a with others could be lower than the future cost of person when connected with another one. Behavior being cheated. On the other hand, when interaction and networks can change dynamically in a complex is between strangers, with no previous experience of regime of possibilities/constraints that could have each other, a set of communication signals or tags dramatic implications for macro behavior. might exist. These in turn could help individuals to Dynamic networks are also important factors in convey and recognize the degree of trustworthiness of establishing trust. Bravo et al.60 calibratedanABM a potential partner and thus risk cooperation. This is on experimental data on the behavior of real sub- the case of taxi drivers and their relationships with jects in a repeated trust game. They compared scenar- customers, brilliantly documented by Gambetta and ios where agents were embedded in exogenously fixed Hamill.53 networks (e.g., random, scale-free, and small-world In order to look at the emergence of trust among networks) and scenarios with endogenous networks, strangers, Macy and Skvoretz54 built a model in which where agents could select their partners according to agents could decide whether to engage or not in a simple happiness function. They found that coop- a Prisoner’s Dilemma game by learning to display eration dramatically increases in dynamic networks. or mimic and recognize actual or fake signals of Trustworthy agents tended to cluster around emerg- trustworthiness and eventually imitating successful ing cooperators, who had more ties and ensured higher strategies from others. They assumed that agents profit to their respective partners. On the other hand, were embedded in a social network structure with ‘bad apples’ tended to be isolated over time losing neighbors and strangers through strong and weak both profit and opportunities for exchange. Further- ties, respectively. Couples were randomly paired with more, while different initial network conditions did a probability correlated with the social distance of not affect this endogenous dynamics (see Figure 2), agents. They tested the effect of different payoffs for with more cooperative agents benefiting from an expo- not engaging in a risky exchange (i.e., an exit option) nential growth of number of ties independently of the and the degree of the agents’ network embeddedness. initial network constraints, the final network topol- Results showed that cooperation between strangers ogy in case of initial random or regular networks was could emerge in the long run, due to less costly exit different (see Figure 3). payoffs that allowed agents to build clusters of trustful These results were confirmed experimentally in relationships locally that gradually diffused via weak an iterated Prisoner’s Dilemma.61 It was also con- ties, depending on the level of agent embeddedness. firmed in a model on a helping game where Chiang62 Following experimental studies on cross-cultural allowed agents to use information of network char- differences on trust and commitment,55 Macy and acteristics (e.g., the structural attribute of the nodes) Sato56,57 tested the effect of spatial mobility on the to strategize whether to cooperate or not. The coevo- emergence of trust and cooperation in a simulated lution of behavior and network created a crystallized

‘exploiters’, i.e., defectors who have a larger payoff 50.0 Dynamic2k10 than the average obtained by cooperators. By endogenously converging toward a small-world topology, the 20.0 network achieved a strong hierarchical structure in which the leaders played an essential role in sustain- 10.0 ing cooperation. On the other hand, they found that once disruptions affecting leaders were introduced, a 5.0 Dynamic2Couples dynamic cascade was found, which propagated defec-

No. of links No. tion throughout the network. 2.0

1. 0 Conventions Social life is full of examples of social interaction 0.5 where it is of mutual interest for individuals to converge toward a dominant behavior, rather than com- 0 20 40 60 80 100 pete on certain rewards at stake. We have devel- Agent number oped certain habits or conventions, e.g., language, | monogamy versus polygamy in marriage, a partic- FIGURE 2 Average number of links per agent in the ular dress code, that help us coordinate with each ‘Dynamic2couples’ (initial random coupling and broken ties were other more or less efficiently. Once established, these replaced by only one of the two formerly linked agents) and ‘Dynamic2k10couples’ (the same but starting from a regular network of conventions can even be institutionally enforced, e.g., degree 10) scenarios (Reprinted with permission from Ref 60, p. 489 traffic rules. The challenge here is to understand the Copyright 2012 Elsevier Ltd). origins of these social artifacts, given that any coordination game may have multiple possible equilibria, configuration where cooperators had more ties and no initial preferable options exist, and outcomes are achieved higher profit so that cooperation outper- extremely sensitive to initial conditions, path depen- formed defection over time. dence, and increasing returns.64 This fact would indicate that social structure can In order to understand this, Hodgson and endogenously generate role differentiation that may be Knudsen65 modeled a population of agents ran- relevant in generating conditions favorable to cooper- domly located in a 100 × 2 cell ring that had to ation. For instance, Eguíluz et al.63 simulated a spatial decide whether to drive clockwise or counterclock- Prisoner’s Dilemma model where diverse social roles wise around a ring to avoid collision. Agents were emerged from dynamic networks with ‘leaders’, i.e., characterized by a limited vision of space, inertia, agents obtaining a large payoff, who were then imi- and a habituation level, i.e., the tendency to repeat tated by many others, ‘conformists’, that is unsatisfied past behavior. Their simulations showed that the cooperative agents, who keep cooperating and finally, convergence of agents toward a right/left convention

(a)Dynamic2Couples (b) Dynamic2k10

FIGURE 3| Networks after 30 rounds of a typical simulation run of the ‘Dynamic2couples’ (a) and the ‘Dynamic2k10couples’ (b) scenarios (Reprinted with permission from Ref 60, p. 488 Copyright 2012 Elsevier Ltd).

However, it is reasonable to presume that the emergence of conventions is also influenced by network effects, i.e., how agents are connected. Many 1.00 studies have examined the influence of exogenous net- 0.95 work structures on the diffusion of conventions.67 It 0.90 is probable that, while engaged in coordination problems, agents try to avoid those who behave differently 0.85 and prefer relationships with agents similar to them- 0.80 selves. The consequences of these endogenous mecha- 0.75 nisms of the formation of a social environment were 0.70 explored by Buskens et al.68 in a repeated coordi- Convergence 0.65 2 nation game model. Here, agents were called on to 0.60 1. 5 decide which opinion to endorse and their payoffs depended on the choices of other agents they were 0.55 1 0.50 Habit tied to. The authors examined the importance of ini- 0.5 0.020 tial network conditions on the emergence of conven- 0.015 0 tions. They found that the density of the network had 0.010 0.005 a crucial impact on the final conventions’ equilibrium. Error 0.000 The more segmented the network was, the higher the likelihood that two groups with different conventions FIGURE 4| Convergence of the population on a shared convention emerged over time. This was due to the fact that cer- for each habituation level and for different error probabilities (Reprinted tain agents preferred to have ties with agents similar with permission from Ref 65, p. 29 Copyright 2004 Elsevier Ltd). The to themselves, rather than adapting their behavior to higher the convergence value, the larger the diffusion of any given dissimilar ones. right/left convention. The importance of these endogenous network formation mechanisms was also confirmed by Corten is higher when the level of habituation increases, inde- and Buskens.69 Their findings from a repeated, pendent of the error at the agent-level when estimating multi-person coordination game model with network other agents’ behavior (see Figure 4). Furthermore, embeddedness were tested in a laboratory experiment. they confronted agents with different cognitive capa- Here, subjects played a coordination game with pay- bilities of monitoring the environment. They found that although habit had a positive effect on the emer- offs depending on the choices of other neighboring gence of conventions even for omniscient agents, agents while they could create, maintain, or break the most striking influence was found when agents their ties depending on a certain cost. Results showed were boundedly rational, thus showing how habit that agents were more efficient in terms of coordina- can complement individuals’ cognitive limitations in tion, where the initial networks were less dense and achieving coordination at a collective level. they could endogenously adjust their networks. Epstein66 built a similar model to investigate the Finally, it is worth noting that these results were link between the strength of a convention and the also empirically tested on a longitudinal survey about cognitive costs that individuals have to pay to decide alcohol use among adolescents in 14 Dutch secondary what to do. He simulated a population of agents in schools, conducted in 2003 and 2004. Here, alcohol a ring, similar to the previous example, which had a use was modeled as a risk-dominant inefficient behav- heterogeneous sampling radius (i.e., space of vision). ior in a coordination game. Adolescents were motivated to align their behavior with that of their friends They could observe other agents’ behavior within their 70 radius and could generalize global attributes by reduc- to be approved socially. While initial alcohol use ing or extending the search process around it. His propensity per class had a positive effect on average alcohol use at a later stage, the initial network density simulations showed that two conventions could coex- 71 ist, with local conformity versus global diversity pat- dramatically amplified this tendency. terns. However, this required considerable cognitive costs for intermediate agents, i.e., agents who contin- SOCIAL INFLUENCE ued to shift from one convention to another one. He also found that when a given convention equilibrium Individuals rarely make decisions in complete isola- emerges, it feeds back to the agent-level by minimizing tion of their social context.72 The influence of social cognitive decision costs, and therefore a macro–micro contexts on individual decisions is something that self-reinforcing path. supporters of rational choice theory often tend to

Volume 7, July/August 2015 © 2015 Wiley Periodicals, Inc. 291 Advanced Review wires.wiley.com/compstats underestimate or conceive simply as information bias. Indeed, any household that reached its threshold and However, in situations of uncertainty, the exposure moved out of its neighborhood reduced the number to social signals from the behavior of other people of similar neighbors in the original neighborhood, might influence our behavior, as we presume that oth- leaving whoever was left closer to its threshold. Any ers know more than we do. At the same time, in group movement of households also changed the receiving life, we know that our behavior is a signal for others neighborhood and indirectly also the neighborhoods who are observing and judging us. This is particularly of the neighborhoods, thus triggering a cascade of important when the opinion of others can influence reactions toward an equilibrium of household distri- our access to important resources, e.g., economic ben- bution far from the original households’ preferences efits and social approval. (see Figure 5). When the decisions of individuals are not If we only looked at the individual level, we independent but interdependent, choices do not sim- could predict macro segregation but with a more ply aggregate at the macro level. This makes any mixed residential distribution. If we only looked at micro–macro or macro–micro mapping potentially the macro level, we should presume the segregational misleading if we do not consider the meso-level preferences of households, which was not the case. between individual choices and social outcomes. This abstract model allows us to understand that For instance, macro patterns can be the result of social context is typically a nexus of interdependence, unintended consequences given that they do not e.g., the choice of A influences the choice of B, reflect individual preferences but only interaction or which influences the choice of C, and subsequently propagation effects. that of A again. This makes it difficult for any linear micro–macro mapping (see also Sakoda8). This reminds us of the classic lessons of complex adaptive Segregation Patterns systems theory: even with simple agent interaction, A classic example of the analysis of social interdepen- there is always a possible gap between individual dence is the famous Schelling’s segregation model.9 choices and aggregate processes so that looking only Here, a population of households of two groups, say at individual levels, whether micro or macro, can lead black and white, was located in a two-dimensional us to draw illusionary conclusions.74 space, characterized by regular neighborhood struc- Thanks to its simplicity and ability to be gen- tures, representing an idealized urban space. House- eralized, the Schelling’s model has contributed to a holds had a threshold preference about the group of prolific stream of ABM research. Certain authors their neighbors and could stay or move randomly have extended this original version by modifying toward new locations in case the number of similar important model parameters, e.g., preference thresh- neighbors was below the threshold. Results showed olds, search for new locations, intentional household that even moderate preference for similar neighbors preferences toward integration, size of the neigh- could tip a society into a segregated pattern. This was borhoods, or spatial network topologies.12,75–79 due to the interdependent nature of choices and their Gilbert80 examined the influence of certain social spatial and temporal effect on changing the context. attributes of neighborhoods, such as crime rate,

(a) (b) (c)

FIGURE 5| Residential segregation in the NetLogo Schelling’s segregation model with household threshold preferences of similar neighbors at (a) 25%, (b) 33%, and (c) 50%.73

292 © 2015 Wiley Periodicals, Inc. Volume 7, July/August 2015 WIREs Computational Statistics Agent-based models in sociology the neighborhoods’ perceived prestige, and certain in whiter neighborhoods than they would otherwise, economic constraints, by providing households with whereas poorer blacks are racially and economi- more sophisticated cognitive processes of social cally isolated. The focal mechanism is called ‘off- environment’s detection. Benito et al.81 provided an setting’: under sufficiently high levels of within-race experimental test of Schelling’s findings in a laboratory income heterogeneity, increasing between-race income experiment. In all these cases, the original findings inequality can have opposite effects at the high and were corroborated and this contributed to make low ends of the income distribution. Whether these Schelling’s model a general example of the unintended offsetting processes cause a net increase or decrease consequences of individual choices in social situations. in segregation depends on the relative size of the black In a recent article, Bruch and Mare82 started population, the salience of racial versus economic fac- from empirical evidence that indicated that individuals tors in residential mobility decisions, and the shape of tend to respond continuously to variations in the racial the income distribution. makeup of their neighborhoods. They replicated the Finally, it is worth noting that Schelling’s find- Schelling’s model, but assumed that households could ings have also been extended into policy and health experience a small increase in the desirability of their fields. For instance, Auchincloss et al.87 showed that location for each given percentage increase in the pro- residential segregation might play a role in deter- portion of similar households in their neighborhood, mining the diffusion of obesity and related illnesses thus removing the threshold shape of households’ in low-income families. By adding food price and preference. Their results showed that linear function preferences and locating stores across the neighbor- preferences could soften residential segregation. hoods in the model, they showed that ceteris paribus, In response to the model of Bruch and Mare, residential segregation alone could increase income van de Rijt et al.83 examined the rules that determined differential in diet, independent of the low-income how households moved when they were unsatisfied. households’ food preferences. Negative implications They showed that in a multicultural population with of residential segregation were also found in public 88 89 integrative preferences, threshold preferences at a goods provision, income distribution, and quality 90 micro level might help to prevent tipping, provided of schools and labor market. that households made mistakes and moved to neighborhoods that did not necessarily correspond to their Cultural and Opinion Dynamics preferences. This presumed that they did not have Although social influence would lead us to expect complete information about the real composition of a dominant tendency toward convergence in collec- the new targeted neighborhood. They showed that tive behavior, social systems often display persistent segregation is likely to occur once agents have a clear dynamics of cultural and opinion diversity. Minority preference toward diversity, move to undesirable beliefs or opinions tend to persist over time, indepen- neighborhoods, or promptly react to the changes in dent of any social force pushing them toward unifor- their neighborhood. On the contrary, once house- mity. This is especially relevant when we observe the holds have a clear preference toward ethnicity, react persistence of collective misbeliefs and discriminatory promptly to their neighborhood’s changes and rarely stereotypes in certain societies or the impact of extrem- make mistakes in selecting their new neighborhood, ist groups in politics. integration is more likely. This indicates that the Influenced by Latané’s social psychological the- shape of preferences does not have unequivocal impli- ory of social impact,91 Nowak et al.92 modeled a pop- cations, but rather that this depends on household ulation of agents in a lattice with randomly assigned preferences. It is worth noting that the importance of binary values of an opinion variable and heteroge- the contextual nature of preferences and the possible neous levels of persuasiveness and supportiveness. heterogeneous nature of neighborhood composi- These levels were defined, respectively, as the abil- tion were also found in an empirical calibration of ity to make out-group agents change their opinion , Schelling’s model in Israel.84 85 and in-group agents to resist outsiders’ persuasive- More recently, Bruch86 calibrated a segrega- ness. Agents changed their opinion value accord- tion model by using empirical data on three cities ing to the relative impact of total persuasiveness in the U.S., the Panel Study of Income Dynamics or supportiveness exerted on them by other agents, and the 1980–2000 U.S. census data. She found that weighted by their distance from the agent within the income inequality affects racial segregation. Given matrix. Simulations showed that, besides the emer- that higher between-group income inequality increases gence of a dominant opinion, the formation of strong the salience of economic factors in residential mobil- local minority clusters prevented in-group agents ity decisions, she found that high-income blacks live being influenced by the majority. This determined the

Volume 7, July/August 2015 © 2015 Wiley Periodicals, Inc. 293 Advanced Review wires.wiley.com/compstats emergence of a polarized stable equilibrium, with local for the persistence of cultural diversity, especially in convergence and global polarization of cultural traits, large populations, as local clusters could better resist due to the high sensitivity of persuasiveness and sup- deviant agent influence under conditions of perturba- portiveness to structural embeddedness factors. tion, and eventually prevent it from spreading globally. This avenue was further explored by Axelrod,13 It is worth considering that the local convergence who built a more sophisticated model to test the effects and global diversity pattern can also be generated of structural embeddedness, cultural heterogeneity, when homophily or social influence is not expected to and interpersonal influence on convergence and polar- play a crucial role. Combining standard game theory ization outcomes. Adaptive agents were modeled with and ABMs, Bednar and Page97 showed that certain heterogeneous cultural characteristics, defined as a structural characteristics of cultural dynamics might combination of a fixed number of cultural features be generated by purposive agents playing multiple (e.g., language, religion, etc.), each taking n possi- games without reacting to evolutionary pressures. ble trait values (e.g., English, German, Italian; Chris- Similarly, Bednar et al.98 showed that a certain level tian, Muslim, etc.). Agents interacted with neighbors of diversity could persist within local cultural clusters. with a probability dependent on the number of iden- By assuming that culturally heterogeneous agents, tical cultural features they shared. A mechanism of besides facing social pressure to conformity, also strive interpersonal influence was added to align one ran- for internal consistency among their own different domly selected dissimilar cultural feature of an agent features, they showed that global convergence could to that of the partner, after interaction. The author emerge in the long run, yet allowed for an intermediate manipulated certain parameters of cultural hetero- phase in which cultural heterogeneity persisted. geneity (number of features and number of traits) and Social influence is also important for the for- structural embeddedness (interaction range and envi- mation and diffusion of political opinions, includ- ronment size). Confirming previous studies, Axelrod’s ing the rise and propagation of minority political simulations showed that global convergence toward positions. By extending previous studies on opinion a single culture did not occur, despite interpersonal dynamics,99,100 Deffuant et al.101 built a model in influence mechanism. Moreover, they showed that the which a continuous opinion variable x (−1 < x < 1) number of emergent cultural groups positively corre- was distributed within a population of adaptive lated with the number of cultural features and neg- agents. In this way, moderate and extreme positions on atively correlated with the interaction range. This a political issue could be contemplated. Agents were was because large-distance interaction amplified the also equipped with an uncertainty value, negatively effect of interpersonal influence from the local to the correlated with the level of the agents’ political radical- global scale. However, cultural diversity was unex- ism, following the assumption that radicals are more pectedly found to negatively correlate with both the confident of their own opinions. Both opinion and number of possible traits and the environment size. uncertainty could change over time through interac- More recently, Klemm et al.93 found that cultural tion, so that agents randomly coupled and influenced homogeneity could eventually emerge due to low rates each other if their opinion distance was lower than of random cultural perturbations, which caused the a threshold, eventually leading to converging opin- collapse of boundaries between otherwise dissimilar ions. The agents’ influence negatively depended on neighbors. Moreover, by looking at the coevolution their level of uncertainty. By manipulating the uncer- of network structure and agents’ partner selection, tainty distribution and the proportion of radicals in Centola et al.94 identified a certain size-dependent the population, they showed that for low levels of perturbation parameter region for which interpersonal uncertainty, the influence of radicals was effective only influence and homophily prevented the evolution of on a small proportion of closer agents, eventually lead- the system into monoculture or unstable global cul- ing to convergence around moderate levels. However, tural diversity. This in turn generated a stable, polar- for high uncertainty levels, radicals prevailed, causing ized global equilibrium. concentration of opinion distribution either on a single However, the unrealistic narrowness of such extreme or on both (bipolarization). parameter region was pointed out by Flache and By adding a social network structure to the Macy,95 who found a stabilizing mechanism for the previous model, Amblard and Deffuant102 showed emergence of a bipolarized global equilibrium. They that extremists could exploit low connected networks questioned the assumption of the dyadic character of better, as they could spread in local clusters and coexist social influence in favor of a multilateral model of with the rest of the population. On the other hand, that mechanism.96 Their results showed that multi- when connectivity increased around a critical value, lateral interaction could be a more robust mechanism the extremists were confined to peripheral regions by

294 © 2015 Wiley Periodicals, Inc. Volume 7, July/August 2015 WIREs Computational Statistics Agent-based models in sociology core moderate agents. Furthermore, Deffuant103 com- emergent interaction structure. However, the overall pared different formal models of opinion and uncer- distribution across multiple issues was not polarized, tainty across three network structures, pointing out except for highly salient takeoff issues. This suggests that extreme convergence was possible in certain net- that individuals’ perception of opinion homogeneity work configurations, which favored the isolation of in local interpersonal networks emerges from grad- clusters of moderates and permitted radicals to influ- ual segregation of interaction partners around takeoff ence other agents without being influenced in turn. political issues, despite the fact that individuals still Polarization can be further influenced by the have heterogeneous opinions about other issues. fact that in social life partner selection might be Furthermore, it is probable that individualiza- driven by xenophobia.104 This implies that negative tion mechanisms besides homophily-driven social interpersonal influence could even exacerbate this influence can affect collective dynamics, i.e., the tendency. In order to consider this, Macy et al.105 tendency of certain individuals to increase their developed a model of adaptive agents with binary own ‘uniqueness’ when their group starts to become cultural states, which were embedded in a fully con- overcrowded.109 For instance, Mäs et al.110 tested nected network of weighted undirected ties. Weights, the effect of individualization on cultural conver- w (−1 < w < 1), incorporated information about the gence by building a simple model with mechanisms strength and the valence (positive or negative) of of choice homophily and nonnegative social influ- the influence between agents in dyadic interaction, ence. By assuming a noise parameter that imposed were randomly distributed among the ties, and could agents’ changes of opinion depending on other similar evolve according to changes in the number of similar agents in the group, they showed that a phase of traits. By manipulating decision-making flexibility stable clusters with diversity between and consensus and the number of cultural states, results showed within tended to emerge. In this same vein, Mäs that a bifurcating network equilibrium emerged. A and Flache111 developed and experimentally tested stable outcome toward homogeneity would not occur a model of homophily and social influence in which unless only positive valence of partner selection and agents interacted through the exchange of arguments social influence were assumed. In a development of instead of adjusting to each other’s opinions. Their this model, Flache and Macy106 tested the effect of results showed that interpersonal communication the bridging role of ‘long-range ties’107 in fostering generated a bipolarized equilibrium but only for high cultural convergence, by allowing agents to create levels of choice homophily. dynamic networks within different exogenous net- This approach has also been applied to diffusion work structures. Results showed that long-range ties dynamics of innovation. Deffuant et al.112 extended did generate cultural homogeneity but only when the continuous opinion dynamic models by simulating interaction was limited to positive selection and influ- agents who held dynamic opinion values about the ence. On the contrary, in cases of bivalent influence, impact of a particular innovation on society—i.e., its long-range ties induced a polarized equilibrium. social value. Agents could collect and share informa- By looking at the U.S. American public opinion, tion for the assessment of expected individual payoff, Baldassarri and Bearman108 investigated the bivalent only when the social value was considered to be nature of partner selection and social influence mech- high enough. Their results suggested that under these anisms to explain the mismatch between perceived conditions, innovations with overall high social value and actual polarization at both local and global level. but low expected payoffs were more likely to succeed They modeled a population of agents with heteroge- than innovations with low social value but higher neous opinions about multiple political issues, attach- individual benefits. Moreover, diffusion dynamics ing different levels of interest to each of them, whose are significantly influenced by at least a minority of sign represented the opinion on them (either posi- radical innovators. tive or negative). Interaction partners were selected More recently, Van Eck et al.113 developed an with a probability inversely depending on the per- empirically grounded ABM to study the effects of ceived ideological distance between the agents. More- opinion leaders on the diffusion of innovation via nor- over, interaction directly depended on the absolute mative and informational influence. The basic con- value of the interest level that agents attached to dif- cept was that agents could adopt innovation stemming ferent issues. Agents then interacted by focusing only from either social pressure or social information about on the issue in which they were most interested and quality. A sample of free online game consumers was could then update their opinions. Simulation results used to calibrate the behavior and position of opinion showed that bivalent selection and influence across leaders. Opinion leaders were situated in central posi- multiple issues caused clustered polarization in the tions within the network. They were more prone to

Volume 7, July/August 2015 © 2015 Wiley Periodicals, Inc. 295 Advanced Review wires.wiley.com/compstats adopt innovations, could assess the quality of a prod- embeddedness to this model. He assumed that agents uct better, and were also less permeable to normative were more influenced by spatially closer connections. influence. By comparing network configurations with He used data on the extraordinarily rapid diffusion of and without opinion leaders, the authors found a sig- trade union organizations in Sweden between 1890 nificant effect of opinion leaders on the rapid spread and 1940 to test this model. Simulations showed that of diffusion. This was because they could spread posi- the spatial-based structures of social contacts could tive information about the quality of the products and explain the empirically observed behavior. were less likely to be affected by the normative influ- A more complex model was elaborated by Kim ence exerted by more conservative agents. and Bearman118 to explain the participation to social movements. Their model showed that there was no Collective Behavior need to assume agents’ irrationality to explain why individuals voluntarily engaged in collective action Our decision to join a social movement or spread a even when this was risky or costly. They simulated cultural fad depends heavily on the effects of social the interaction between agents with different interest influence. This is because we are often influenced levels in providing a public good—from whose ben- by observing other people’s behavior before decid- efits no agents could be excluded—and the different ing what to do. It is often difficult to understand amounts of resources to produce it, which shaped a empirically how certain collective behavior are pro- dynamic network. Agents decided whether or not to duced when individuals are subjected to social influ- contribute according to the expected marginal ben- ence without analyzing the effect of social structural efit, which they calculated upon their interests, the factors, such as complex network configurations. cost of participation, and the amount of resources In this field, a seminal model was published by they possessed. However, the agents’ interest in the Granovetter,114 who analyzed the dynamics of a type good varied either upward or downward depending of collective behavior, such as a riot, by simulating on whether their ties had previously contributed or agents deciding whether to join it depending on the defected. By manipulating various structural parame- decisions of other agents. Agents were modeled to ters, simulations showed that a critical mass of highly make a binary choice, according to an expected benefit interested agents situated in central network positions, dependent on a heterogeneously distributed threshold even if guided by self-interest, could create a local value of how many agents were already participating. dense cluster, which eventually neutralized the influ- In a simulation scenario, he added the impact of ence of defecting agents. In particular, network density previous decisions of relevant agents connected to the was more decisive to achieve this critical mass than individual. His results showed that whenever network high concentration of resources. externalities are added, collective behavior becomes Chwe119 proposed a model in which strate- extremely dependent on nonlinear dynamics, which gic agents chose to participate in a collective action makes it very difficult to predict macro behavior on depending on the expected number of participants single individual preferences. among their neighbors. Consequently, expectations of Threshold models of collective behavior have neighbors’ participation depended in turn on expec- also been used to analyze innovation diffusion dynam- tations of neighbors of neighbors’ participation and ics. By integrating Granovetter’s classic model with so on. The agents were assigned a fixed number of a network structural component, Abrahamson and , partners for the whole simulation cycle. By examining Rosenknopf115 116 looked at the differences in band- the effect of network transitivity on social influence, wagon effects due to certain network communica- results showed that transitivity was particularly effec- tion properties. They found that bandwagon effects tive in triggering bandwagon effects among agents in innovation diffusion within a network also depend with low thresholds, as they could get information on particular structural characteristics of nodes that from locally small and yet dense clusters. For agents bridge core and peripheral components and the perme- with high thresholds, however, weak ties were espe- ability of their boundaries. Furthermore, by weighting cially important as they transmitted information about social influence with exogenously distributed opinions a larger amount of agents. about the reputation of innovations, they showed that bandwagon effects could override information about their unprofitability, eventually leading agents to con- Social Inequality verge on inefficient practices. It is probable that social influence is responsible Hedström117 relaxed Granovetter’s original for a variety of dysfunctional collective patterns assumption of homogeneity of interpersonal influence typically observed in macro quantitative sociology. and added the more realistic dimension of spatial These include inequality in educational opportunities,

296 © 2015 Wiley Periodicals, Inc. Volume 7, July/August 2015 WIREs Computational Statistics Agent-based models in sociology social stratification, employment traps in the labor Analytical theories explain the emergence of status market, and the coevolution of social and workplace hierarchies caused as a result of a self-reinforcing segregation.120 process driven by the exchange of deference- For instance, by looking at the labor market, conferring gestures (i.e., the attribution of a per- Hedström and Åberg121 built an empirically calibrated ceived quality evaluation). This amplifies the already ABM to examine how social influence mechanisms existing qualitative differences between individuals.124 can explain aggregate youth unemployment rates. Recently, Manzo and Baldassarri125 tested the poten- Their hypothesis was that levels of unemployment tial inequality driving effect of social influence on among neighborhood peers had an effect on youth status attribution mechanisms, by hypothesizing a unemployment by lowering their expectations of counteracting effect of reciprocity in the exchange finding a job, reducing the psychological costs of of deference-conferring gestures. They modeled a being unemployed, and preventing outsiders access- population of agents with heterogeneously distributed ing insider information about job opportunities. ‘quality’ values, assessing each other’s quality and Large-scale observational data on youth unemploy- exchanging deference gestures. In addition, they ment in Stockholm between 1993 and 1999 were used could become biased by other agents’ behavior. The to calibrate the socio-demographic characteristics of agents interacted on the basis of status homophily, individuals and the structural features of the neigh- by selecting partners within an acceptable range of borhood network clusters. Transition probabilities of status dissimilarity (corrected by a heterogeneously leaving unemployment were also estimated through distributed ‘heterophily’ constant). They also assessed maximum likelihood statistical modeling. The authors partners’ quality, by considering the partner’s pre- assumed that agents decided to leave unemployment viously acquired status, their own tendency to rely according to their own socio-demographic character- on social influence, and a noise value. Subsequently, istics, the unemployment rate in their neighborhood, the agents transferred a deference value to their and the tightness of the job market. Simulations interaction partners, which was equal to the part- showed that the combination of social influence and ner’s perceived quality, unless the evaluating agent agents’ educational level provided the most strik- had previously received less deference than expected ing effect on the population’s rising unemployment from the partner. In the latter case, according to a rate. Furthermore, the effect of social influence was heterogeneously distributed parameter for sensitivity comparably higher than that exerted by the agents’ to reciprocity, the evaluating agent reciprocated the educational level per se. partner’s previous unfair behavior by exchanging When looking at social stratification, it is likely less deference. Status values were then calculated that there is a persisting effect of social origin for each agent as the average deference received. on educational attainment, which has traditionally The simulation results suggested that the interaction been explained through rational choice approaches.122 between the cumulative effects driven by social influ- Recently, Manzo123 proposed an ABM to improve the ence and the counterbalancing effect of conditional realism of standard rational choice models by intro- deference exchange was sufficient to generate status ducing a social influence mechanism within friendship hierarchies, which are qualitatively similar to those networks. Agents were assigned into four groups, rep- observed in empirical research, that is, the increasing resenting background social classes. They were then gap between actual quality and status asymmetry. embedded in a small-world network and allowed to Furthermore, if low-status agents were more prone take decisions about transitions from an educational to have mixed interaction with similar and dissimi- level to the next one. These decisions were based lar agents rather than high-status agents, outcomes on the evaluation of their own ability, the perceived tended toward a ‘winner-takes-all’ status hierarchy. cost/benefit ratio, their probability of success in func- Finally, Gabbriellini126 built an empirically tion of their ability, and the effect of the overall social tested model of the emergence of status hierarchies influence exerted by others with whom they were tied. in task-oriented groups as the effect of a network Simulation findings were tested against observational of precedence ties.127 He modeled the interaction data about the French stratification of educational within a disconnected network of agents, who could choices across social origin in 2003. Results showed participate in a discussion with other members by that only by considering a social influence mechanism addressing precedence claims in the hierarchy to all could the model generate outcomes sufficiently close others (i.e., asking everyone to accomplish a task). to the empirical data. Agents’ participation depended log-linearly on the Another interesting field includes the study of the expected consequences of their claim. Permanent effects of social influence on the reproduction status. precedence ties were established with a probability

Volume 7, July/August 2015 © 2015 Wiley Periodicals, Inc. 297 Advanced Review wires.wiley.com/compstats that partially depended on comparing agents’ exter- account for the subtle social nuances that characterize nal status values, which were activated according individual behavior in social contexts. In this respect, to a probabilistic value. He collected empirical data Gintis129 suggested that we question the aprioristic on communication in an online task-oriented dis- assumption of common knowledge that lies behind cussion forum of a role-playing game community. standard game theory. If we assume that individu- His simulations showed that highly linear status als are rational and self-interested as they perceive hierarchies—similar to those observed—were due to their counterparts to be, game equilibria of any social the higher participation of agents in communication or economic exchange can be predicted. The prob- and the deference generated by mutual observation of lem here is that experimental research has repeatedly external status. found that social outcomes are better explained if we recognize that people develop an ‘epistemic knowledge’ within the game based on implicit ‘shared mind’ DISCUSSION AND CONCLUSIONS efforts. Culture, social norms, and learning as social This article presented a number of sociologically scaffolds for individual rationality make a wider set relevant ABM studies that explain complex social of behavior ‘rationalizable’, which would otherwise be outcomes as effects of agent interaction. Table 2 far from standard self-interest (see also neuroscientific 130 summarizes the most important contributions and research on the positive role of emotions ). provides a systematic overview on their main explana- Behavioral game theory could help explore tory achievements. These cases combine abstract departures from standard rational choice models. models, which look at general mechanisms of social Furthermore, it can be used to understand social phenomena, such as cooperation and social norms, norms in well-controlled experimental scenarios, with middle-range models where specific social puz- relevant for sociological research. By concentrat- zles are analyzed, such as youth unemployment and ing on interaction situations where self-interest is education. Although the prevalence is for theoretical expected to prevail, we can understand the genesis approaches, some empirical applications of these of social norms, their dynamics in terms of fragility models also exist, where important behavioral or or robustness, and the factors that could condition structural model parameters have been calibrated their evolution. This is impossible if we assume that with available or ad hoc–generated empirical data. individuals have no individual autonomy (also that In these cases, such models have been used to com- of being self-interested) and thus passively internalize plement empirical data by manipulating certain norms by culture, education, or social conformism, as parameters (e.g., complex social networks) that in many standard sociological accounts. would be difficult to observe empirically,60 or used Interestingly, most ABM studies mainly look at to generate empirically tested hypotheses.69 In other the self-organization of social groups around social cases, models have been used to reproduce certain norms and should not be seen as a naive exercise. No macro empirical regularity by a given theory.123,126 one believes that institutions and top-down influences Although most sociologists shrink from abstract, simply do not exist. At the same time, the ABM formalized theories, these examples show that abstrac- approach is not a bottom-up ‘market’ ideology. By tion can have a crucial role for theory building even in focusing on micro–macro aspects, ABM studies can sociology when it is guided by modeling. On the other offer relevant insights on how groups and communi- hand, empirically grounded studies are fundamental ties can coordinate and collaborate in our world. This to explain well-studied sociological puzzles and stim- is more and more fragmented into cultures, contexts ulate cross-methodological approaches with mutual and domains, and in constant evolution and change. benefits between, for example, standard quantitative This is to say, the ABM approach is also sociologically sociology and ABMs. Furthermore, this type of study timely and can contribute to understanding social is pivotal in persuading traditional sociologists about change. the advantages of this approach. These ABM studies show that, if we consider At a substantive level, these examples show that society as an evolutionary system in constant change exploring the fundamental heterogeneity of individual and adaptation, the coexistence of different behav- behavior is of paramount importance to understand iors and norms over time is instrumental to pro- the emergence of social patterns. Cross-fertilization mote and maintain social order. This means that between experimental and computational research is institutional policies, which typically assume that indi- a useful process. It shows us that by conflating the viduals are self-interested, end up eliciting self-interest concept of rationality with that of self-interest, as in people. This situation could actually worsen the in standard game theory and economics, we cannot long-term sustainability of social systems for the

298 © 2015 Wiley Periodicals, Inc. Volume 7, July/August 2015 WIREs Computational Statistics Agent-based models in sociology of dyadic interaction patterns from initially random encounters (‘shadow-of-the-future’). intermediate levels of aspiration. cooperation in a competitive environment as it helps to avoid cascades ofreciprocity mutual or defection. trust. instrumental to sustain cooperation. Not onlyrelevant individual for evolutionary traits but social also selection. group characteristics are provided that there is a largecosts number and of network local embeddedness. clusters of trustful relationships. This is due toaccording low to exit their previous experience, independent of the initial network structure. Norms can help to save the cognitive costs of decisions. network structures, but rather can interactinitial within behavioral a tendency dynamic of network. the Network population.young density This people’s amplifies can friendship the explain networks. the diffusion of alcohol abuse within capabilities and more effective than directreputational experience information in quality. detecting reliable partners, independent of Socially sharing false bad reputation sustains cooperation more than false good reputation. Cooperation can emerge if interaction and reproductionIn-group are bias constrained and locally. tags can sustain cooperation even without direct reciprocity. Under uncertainty and information asymmetry, sharing reputation is beneficial for agents’ exploration Explanatory Manipulation Main Findings T) E, = = T Micro In two-person social dilemmas, cooperation can emerge among backward-looking agents with E Both Trust and cooperation among strangers dramatically increase if agents can select exchange partners T, T Micro The mix of self-interested agents, altruistic agents, and strong reciprocators at a group level is Approach (Empirical Theoretical learning dynamic and group selection selection Direct reciprocityDirect reciprocity and T, TEthnocentrism Macro T, T, T, T Cooperation among forward-looking self-interested agents canCommitment evolve as a pure effect of the Micro persistence Reputation The evolution of cooperation can be sustained by the emergence of an in-group-biased T dominant strategy. T, EStrong Micro reciprocity Even a moderate form Micro of commitment canTrust be and more signaling efficient than direct Socially reciprocity sharing in sanctioning sustaining costs provides more evolutionary stability for cooperation than direct Trust and partner TConventions MacroCoordination Cooperation can emerge in the long run if T, agents T follow signals of trustworthiness for partner selection, T, E, E Micro An Both efficient coordination norm can also emerge with minimally rational agents, An if efficient they coordination can norm rely can on emerge habits. if homophily-driven agents are not constrained in exogenous 65 ; 71 69 40 54 45 29 30 68 22 26 20 , 39 60 Summary of the Most Sociologically Relevant ABM Studies 23 47 25 66 27 24 Corten and Knecht Axelrod ReferenceCohen et al. Macy and Flache Topic Bausch Back and Flache Macy and Skvoretz Buskens et al. Riolo et al. Axelrod et al. Hales Conte and Paolucci Boero et al. Boyd et al. Bravo et al. Epstein Hodgson and Knudsen Corten and Buskens Hammond and Bowles and Gintis TABLE 2

Volume 7, July/August 2015 © 2015 Wiley Periodicals, Inc. 299 Advanced Review wires.wiley.com/compstats aggregation. Even multiculturalist preferences can leadsensitive to to residential small segregation changes patterns in if neighborhoodsegregation they composition. can are If occur agents from have the multiple, nonlinearsalience correlated interaction of attributes, between ethnic income versus inequality, economic population factors. size, and explained by homophily and interpersonal influence.brought In about large by populations, multilateral cultural social diversity influences,local can which clusters. be prevent deviant agents spreading out within agents can influence each other and uncertainty is high, especially within sparse networks. homophily and positive influence. Small-world networksinteraction can is generate limited cultural to homogeneity positive only selectionemerge. if The and bivalence influence; of otherwise, selection a and bipolarizedactual influence equilibrium polarization can tends of explain to public the opinion. mismatch between perceived and and peripheral components, leading to possibleinformation convergence about toward social inefficient value outcome. and When profitabilitylow are payoffs decoupled, are innovations more with likely high todiffusion. social succeed. value Opinion but leaders play a significant role in the rapidity of are situated in central network positions,Network even transitivity if can they be do effective not in control triggering a bandwagon significant effects amount among of low-threshold resources. agents. and inequality in educational opportunities inthe industrialized self-reinforcing countries. outcome Status of hierarchies deference can gestures emerge exchange as and social influence. Explanatory Manipulation Main Findings T) E, = = T, E, T Both Opinion bipolarization can emerge if agents conform to xenophobia and negative influence, besides Approach (Empirical Theoretical and negative influence Segregation T, ECultural diversity T, Both T, TOpinion dynamics The interdependence of choice can lead to unintended macro consequences Both due T, T, to T nonlinear dynamics of The persistence ofOpinion local dynamics convergence and global cultural diversity in Macro human societies cannot be fully Political opinions can converge toward one or both extremes, due toInnovation the diffusion presence of a radical minority, if T, T, T, E MacroCollective behavior Innovation can spread as a bandwagon effect within networks with permeable boundaries between core Social T, T stratification E, E, T, E Macro A collective action can Both arise between self-interested agents if a critical mass of Social highly influence interested can agents explain variations over time in youth unemployment rates within urban environments 121 118 95 106 83 116 115 101 112 125 113 94 93 108 126 102 Continued 105 100 123 86 119 Deffuant Rosenknopf Baldassarri Krause Bearman Abrahamson ReferenceVan de Rijt et al. Klemm et al. Topic Flache and Macy Deffuant et al. Amblard and Macy et al. Flache and Macy Abrahamson and Deffuant et al. Van Eck et al. Kim and Bearman Hedström and Åberg Manzo and Gabbriellini Bruch Centola et al. Hegselmann and Baldassarri and Rosenknopf and Chwe Manzo TABLE 2

300 © 2015 Wiley Periodicals, Inc. Volume 7, July/August 2015 WIREs Computational Statistics Agent-based models in sociology following reasons: Firstly, they do not nurture diver- researchers are asked to make models public so that sity and heterogeneity of behavior; and secondly, they replication and model extension are easier. This can can crowd out preexisting social norms and intrinsic increase the cumulative findings and create the collec- motivations.131 In these cases, ABM studies could be tive dimension of any rigorous scientific endeavor.2 used to understand when incentives, regulations, and ABMs can promote a modeling attitude in soci- external institutional design can work, when social ology, including more disciplined theory building and norms are beneficial and when institutions and social a stronger ‘testing hypotheses’ experimentalist cul- normscanworkinsynergy. ture (Box 1). Moreover, they can make sociology a Moreover, these ABM studies can help us to more collective effort by undertaking the path fol- understand the importance of social contexts even lowed by more mature disciplines. In this regard, it when looking at individual behavior in a more is worth noting that there is still a serious gap in micro-oriented perspective. The role of social influence and the fact that we are embedded in complex BOX 1 social networks have implications for the type of information we access and the types of behavior we are exposed to. At the same time, individual behavior ABM PLATFORMS FOR SOCIOLOGISTS has a constructive role in endogenously shaping these Various software platforms are available for networks. While the literature on social networks typ- sociologists to build ABMs. The primary ones ically looks at structural factors, the ABM approach are open-source and have been constantly can enrich the behavioral counterpart of these studies, developed by large user communities. They providing a more dynamic picture of the interplay of provide researchers with speciﬁc developing individual behavior and networks. This could help tools, graphic user interface, and libraries to us to understand the evolutionary bases of network implement various programming languages. structures, ideally considering a complex set of recip- Swarm was the forefather of all ABM platforms. rocal influences between micro and macro levels. It was developed in the early 1990s by an inter- It is worth noting that this interplay is difficult to disciplinary team at the Santa Fe Institute. It understand using standard social science approaches, has implementations in Objective C and Java given that a combination of qualitative and quan- (http://www.swarm.org). Another popular platform is Repast (http://repast.sourceforge.net/), titative factors must be considered simultaneously. which was developed by a team at the University Furthermore, simulations can provide a vivid picture of Chicago and has implementations in vari- of space and time processes that might unfold over a ous object-oriented languages, e.g., Java, C++, long time, also supporting intuitive understanding of Microsoft .NET, and Python. It also allows GIS the complexity of social systems. programming and the creation of sophisticated Here, the advent of the big data movement and visualizations. It is well documented and used the increasing convergence between data platforms in by a growing user community. Models with Java various domains of social life (e.g., the public, pri- can also be programmed with MASON (http:// vate, and social sectors) could allow sociologists to cs.gmu.edu/~eclab/projects/mason/), which was have fine-grained, large-scale data not only on indi- developed by a team from George Mason vidual choices but also on social network connections University. Finally, developed by a team at that were impossible even to contemplate before. By Northwestern University (Chicago, U.S.A.), Net- applying sociologically informed computational mod- Logo128 (https://ccl.northwestern.edu/netlogo/) els to these multisource, layer data, we could reveal the is currently the most famous ABM platform, complex mechanisms of social life in a globally inter- although it is not based on an object-oriented connected world.132 programming language. It provides an inte- Finally, one of the most important sociological grated modeling environment based on its own advantages of ABMs is that they can help sociologists programming language, a dialect of Logo (an to achieve more rigorous standards of theorization educational programming language, originally and empirical analysis. ABM studies have developed a designed to train youngsters). NetLogo can be ideally considered as the best solution to start serious methodological debate on standards in order learning ABMs as it is user-friendly, well doc- to improve empirical calibration and validation of umented, and has a large set of ready-to-use models, model documentation and reporting, and 133,134 models, including some of the classic studies model replication and test. Tools such as a mentioned in this article. It is also the most com- public repository of models have been developed monly used platform for educational purposes. (e.g., ABM Open: http://www.openabm.org/), where

Volume 7, July/August 2015 © 2015 Wiley Periodicals, Inc. 301 Advanced Review wires.wiley.com/compstats computing skills in the education programs of soci- cutting-edge, collaborative research. This is also essen- ologists at all levels, from Bachelors to PhD courses, tial for sociologists to collaborate and compete with and even in top institutions. We need to fill this gap in external experts, who are increasingly performing rel- order to equip a new generation of sociologists toward evant sociological research.

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