Signals and the Structure of Societies University of T¨ubingen Department for General Linguistics Dissertation in Linguistics by Roland M¨uhlenbernd Promotor: Professor Dr. Gerhard J¨ager T¨ubingen,2013 . - Contents Contentsi Acknowledgementsv Introduction1 1 Signaling Games9 1.1 Definition of a Signaling Game................. 12 1.2 Strategies, Equilibria & Signaling Systems.......... 14 1.3 The Horn Game......................... 17 1.4 Repeated Games ........................ 21 1.5 Conclusion............................ 23 2 Update Dynamics 25 2.1 Evolutionary Dynamics..................... 27 2.1.1 Symmetric and Asymmetric Static Signaling Games . 28 2.1.2 Evolutionary Stability ................. 30 2.1.3 Replicator Dynamics.................. 31 2.1.4 The Lewis Game in Evolution............. 33 2.1.5 The Horn Game in Evolution ............. 36 2.1.6 The Plausible Symmetric Horn Game......... 43 2.2 Imitation Dynamics....................... 48 2.2.1 Imitate the Best..................... 48 2.2.2 Conditional Imitation.................. 50 2.2.3 Comparing Replicator Dynamics and Imitation . 51 2.2.4 Integrating Network Structure............. 53 2.2.5 Imitation on a Grid: Some Basic Results . 55 2.3 Learning Dynamics....................... 57 i ii CONTENTS 2.3.1 Languages, Learners and Stability........... 59 2.3.2 Reinforcement Learning ................ 63 2.3.3 Belief Learning ..................... 65 2.3.4 Memory Size and Forgetting.............. 68 2.3.5 Learning in Populations: Some Basic Results . 69 2.4 Conclusion............................ 72 3 Social Networks 75 3.1 Network Properties....................... 76 3.1.1 Node Properties..................... 76 3.1.2 Structural Properties.................. 79 3.2 Network Types ......................... 83 3.2.1 Regular Networks.................... 83 3.2.2 Random Networks ................... 85 3.2.3 Small-World Networks................. 87 3.3 Network Games......................... 91 3.3.1 The Choice for Communication Partners . 92 3.3.2 The Social Map..................... 94 3.4 Conclusion............................ 97 4 Emergence of Regional Meaning 99 4.1 Causes for Regional Meaning..................102 4.1.1 Dynamics and Game Parameters . 105 4.1.2 The Degree of Locality . 120 4.1.3 Further Influences....................128 4.1.4 Interpretation of the Results . 131 4.2 Border Agents Analysis.....................134 4.2.1 Border Agents Arrangement . 134 4.2.2 Border Agents Behavior . 137 4.2.3 Extreme Initial Conditions . 138 4.2.4 The Convex Border Melting Phenomenon . 141 4.2.5 Summary ........................143 4.3 Conclusion............................144 5 Conventions on Social Networks 147 5.1 Small-World Experiments ...................148 5.1.1 Language Regions & Agent Types . 149 5.1.2 Lewis Games on β-Graphs . 152 5.1.3 Lewis Games on Scale-Free Networks . 162 CONTENTS iii 5.1.4 Horn Games on β-Graphs . 171 5.1.5 Horn Games on Scale-Free Networks . 175 5.2 Conclusion............................180 6 Summary 185 6.1 How Do Linguistic Conventions Arise? . 186 6.2 What Causes Regional Meaning? . 188 6.3 Why is the Horn Strategy Predominant? . 189 6.4 Conclusion............................191 7 Zusammenfassung 193 Bibliography 195 A Proofs 205 Acknowledgements Networks have played an important role not only in this dissertation but also in my life. It has therefore been an honor to be a node in the larger network of collaborators, all of whom have supported me in completing this dissertation. Although there is no way to make an exhaustive list, I want to thank Anton Benz, Armin Buch, Stefano Demichelis, Christian Ebert, Fritz Hamm, Elliott Wagner and all my colleagues for support and enlightening discussions, especially in the fields of game theory and pragmatics, language evolution and change, network theory and phenomena from sociolinguistics. I should also mention our very supportive and lively department (Special thanks to Christl!). My thanks go to them not only for their professionalism but also for their congeniality. In that regard, I would also like to thank my students, especially those from courses like SLANG and PENG, courses that both inspired some of the ideas seen herein. In closing, special thanks go to three persons that were not only the most prominent supporters of this work, but also good friends. First, I want to thank my doctoral advisor Gerhard J¨ager. It is a privilege to have an advisor who has not only a research record of astonishing diversity, but also an excellent nose for new research directions. I am, in particular, thankful for i) the encouragement to break new ground with my research and ii) the freedom to do so. Both of these factors resulted in an excellent work environment. Second, I want to thank Michael Franke for a productive and engaging collaboration, especially during his stay in T¨ubingen.He was an excellent mentor and the reason for much of my thesis coming into being. Thanks for your encouragement, Micha! And finally, I want to thank Jason Quinley for amazing support in matters both professional and personal. Our track of job-related and private journeys through Europe and the United States was extensive and full of exciting times. Thanks for all your help! v Introduction "A name is a spoken sound significant by convention... I say 'by convention' because no name is a name naturally but only when it has become a symbol." Aristotle 1984, De Interpretatione "[w]e can hardly suppose a parliament of hitherto speechless el- ders meeting together and agreeing to call a cow a cow and a wolf a wolf." Russell 1921, The Analysis of Mind My Ph.D. project investigates the question of how linguistic conventions arise and stabilize. To that end I will examine the emergence of conventional signaling in the spirit of Lewis(1969) who sought an answer to the question: how can linguistic meaning emerge as a convention among language users, assuming no previous explicit agreements? I would like to elucidate this puzzle here. Consider the following three propositions: 1. A convention is exclusively determined by an explicit agreement 2. Human language is a system that consists of linguistic conventions 3. Language, even in the simplest case, is needed to make agreements Standing by these three propositions, we would come to a paradox: lan- guage is needed for language to emerge. As a consequence, one of these propositions must be wrong. While philosophers like Quine took the view that the second proposition must be wrong and thus language cannot be conventional, Lewis paved another way for a solution by claiming that the 1 2 Introduction first of these three propositions is wrong: conventions are not exclusively determined by explicit agreements; conventions, and particularly conven- tional linguistic meaning, can arise without such agreements. He illustrated his claim by constructing and providing a model that formalizes the way conventions can arise without explicit agreements, namely by the emergence of regularities in (linguistic) behavior. The Character of Conventions What characterizes a convention? A natural starting is that it is determined by an explicit agreement. Promises, contracts or rules accepted and followed by all parties among whom the convention holds are examples. In other words: a convention is characterized by its origin. This characterization is e.g. according to Quine(1966), who once asked: "What is convention when there can be no thought of convening?" In fact, there are many conventions that originated by explicit agreement (e.g. to drive on the right or left lane of the street), even for linguistic meaning (e.g. to christen a person or a ship, to invent a word for a new product), but apart from that, conventions in language use are usually not the offspring of agreements once made. This is supported by Russell(1921), who, while dealing with the puzzle of the evolution of linguistic meaning, once argued: "we can hardly suppose a parliament of hitherto speechless elders meeting together and agreeing to call a cow a cow and a wolf a wolf." Thus while philosophers like Quine questioned the fact that linguistic meaning is based on conventions, Lewis questioned the way these philoso- phers defined conventions. Should a convention really be characterized by its origin? He denied this claim and suggested that while the origins of a convention can be multifarious, there are other conditions that uniquely characterize a convention. Lewis's definition of a convention looks roughly as follows: Definition 0.1 (Convention). A convention C is a behavioral regularity among a population with the following properties: 1. common knowledge: every member conforms to C and every member expects everybody else to conform to C 2. arbitrary: C is not determined by nature, but by society 3. alternative: C has at least one excluding (and probably competing) alternative C0, it could be replaced with Introduction 3 To give an example: a behavioral regularity that fulfills these condi- tions is to drive on the right lane of the street: i) it is common knowledge among the population that everybody behaves according to it, ii) it is not determined by nature and iii) it has an alternative: driving on the left lane of the street. Thus according to Lewis's definition, it's a convention. A counterexample that fulfills at least the first condition is to breathe: i) it is common knowledge that every living being breathes. But condition 2 and 3 are violated: ii) it is determined by nature: from birth on we breathe; and iii) the only excluding alternative would be not to breathe which is not a serious alternative. Let's see if the conditions hold for linguistic meaning: to use a specific verbal expression for describing a matter i) is used by all members of the same language area; and it is also known by all members that everybody else inside this language area uses it; ii) is not given by nature, but in gen- eral completely arbitrary; and iii) has practically an unlimited number of alternatives, namely any other verbal expression a society could convention- ally use for that matter.