Bounded Rationality and Endogenous Preferences Robert Östling Dissertation for the Degree of Doctor of Philosophy, Ph.D. Stockholm School of Economics Keywords: Bounded rationality, cognitive dissonance, cognitive hierarchy, endogenous prefer- ences, ethnic diversity, income inequality, level-k, moral values, Poisson games, political polarization, pre-play communication, quantal response equilibrium, redistribution, self-serving bias, social identity, size of government. c EFI and Robert Östling, 2008 ISBN 978-91-7258-757-1 Printed by: Elanders, Stockholm 2008 Distributed by: EFI, The Economic Research Institute Stockholm School of Economics P O Box 6501, SE-113 83 Stockholm www.hhs.se/e… To all of you who let me play in my corner of the sandbox Contents Introduction 1 Papers 7 Paper 1. Communication and Coordination: The Case of Boundedly Rational Players 9 1. Introduction 9 2. Model 15 3. Extensions 24 4. Evidence 29 5. Concluding Remarks 30 Appendix 1: Characterization of Behavior 32 Appendix 2: Proofs 37 References 41 Paper 2. Strategic Thinking and Learning in the Field and Lab: Evidence from Poisson LUPI Lottery Games 45 1. Introduction 45 2. Theory 48 3. The Field LUPI Game 58 4. The Laboratory LUPI Game 66 5. Learning 73 6. Conclusion 77 Appendix A. The Symmetric Fixed-n Nash Equilibrium 80 Appendix B. Proof of Proposition 1 84 Appendix C. Computational and Estimation Issues 86 Appendix D. Additional Details About the Field LUPI Game 94 Appendix E. Additional Details About the Lab Experiment 99 References 106 Paper 3. Economic In‡uences on Moral Values 111 1. Introduction 111 2. Model 113 3. Empirical Analysis 118 4. Concluding Remarks 124 Appendix: Comparative Statics 125 Appendix: Description of Data 128 References 130 xi xii CONTENTS Paper 4. Identity and Redistribution 133 1. Introduction 133 2. General Model 137 3. Black and White Model 143 4. Ethnic Diversity 147 5. Income Inequality 151 6. Ethnic and Class Hostility 153 7. American Exceptionalism 155 8. Concluding Remarks 156 Appendix: Proofs 157 References 162 Paper 5. Political Polarization and the Size of Government 167 1. Introduction 167 2. Related Literature 169 3. Data and Measurement 172 4. Results 180 5. Other Questions 187 6. Conclusion 188 Appendix 189 References 194 Introduction The standard approach in economics takes preferences as given and assumes that eco- nomic agents make rational decisions based on those preferences. In this thesis I relax both assumptions in a number of economic applications. These applications are some- what diverse and belong to di¤erent …elds of economics— game theory, microeconomics and political economics— but they can all be viewed against the backdrop of recent developments in behavioral economics. The growth of behavioral economics took o¤ in the late 1990s as a critique of neoclassical economics, which generally viewed man as self-interested and rational. Although few economists probably wholeheartedly ever believed that all of us are eco- nomic men, until recently, the core of economic theorizing relied mainly on that view of human behavior. This has changed and there are now plenty of economic models based on the alternative assumptions that individuals are imperfectly rational or care for others. The …rst generation of papers in behavioral economics focused on con- vincing other economists that self-interest and perfect rationality are not always the best descriptive assumptions. The second generation of papers in behavioral economics explores the implications of those alternative assumptions about human behavior in various economic settings. I hope that most of the papers in this thesis belong to the second generation and I think this is most clear in the …rst paper of this thesis. In the …rst paper, which is written jointly with my much appreciated advisor Tore Ellingsen, we use a model of bounded rationality in order to better understand a clas- sical question in game theory, namely how communication a¤ects behavior in strategic interactions. Thomas Schelling discussed communication in games already in 1960 in his book The Strategy of Con‡ict. He described the cold war between the US and the Soviet Union as a simple two player game (see Chapter 9 in The Strategy of Con‡ict). Either side could choose to start a nuclear attack or not to attack. Both would be better o¤ if no side attacked, but if one side attacks, the other side would like to do so as well. Game theorists recognize this game as a Stag Hunt— named after Jean- Jacques Rousseau’sdescription of a hunt— a game that has two equilibria: one good, but risky equilibrium where both sides stay calm, and a bad equilibrium in which both sides attack. The most interesting— and challenging— question with this game is to understand which equilibrium that will prevail and whether communication between players can help them to obtain the good outcome. In retrospect, we know that there was no nuclear war, which may partly be due to the existence of the hot line between Moscow and Washington. In the last chapter of Arms and In‡uence from 1966, Thomas 1 2 INTRODUCTION Schelling discussed the hot line more in depth and concluded that communication in- creases the chances that a nuclear war can be avoided: “The hot line is not a great idea, only a good one. (p. 262)” Imagine yourself in the shoes of John F. Kennedy and that you receive a call from Nikita Khrushchev who tells you that today he and his close friend Fidel Castro is not going to start a nuclear war against you. Should you believe him? Initially, the consensus among game theorists was that you should since the message is self- committing, that is, if Mr. Khrushchev thinks that you believe the message, it is in his best interest to do what he said and not attack. However, Robert Aumann pointed out early on that Mr. Khrushchev’smessage is not self-signaling. If he for some reason has decided to start a nuclear war, although that is a worse outcome than no war, then he would have told you that he wasn’t going to attack (since a surprise attack is better than a full scale nuclear war right from the start). Although this line of reasoning seems theoretically sound, experiments have shown that communication often is successful in getting people to coordinate on the good outcome. One of the …ndings in the …rst paper is that when players are boundedly rational it makes sense for President Kennedy to believe in Mr. Khrushchev. The notion of bounded rationality used in the …rst paper is based on the steps of reasoning that many people do when they think about how to act in strategic situations. The kind of thinking that we model goes roughly along the following lines: What if Khrushchev is completely irrational? Most likely, he’sgoing to naïvely say what he is going to do, so I might as well believe him. But what if he is not completely irrational? Then he would …gure out that I would believe his message, so he’s going to be truthful and I better believe him. This way of thinking about bounded rationality goes under the name of level-k rea- soning and has been used to explain behavior in a wide range of experiments. The …rst paper applies that model to communication in games and argues that it provides a better account of how real human beings communicate than the perfectly rational model. The second paper focuses on a di¤erent and much debated question in game theory, namely to what extent mixed equilibria are reasonable descriptions of behavior. In a mixed equilibrium, players attach probabilities to (some of) the strategies they have available and randomize based on those probabilities when they play. Typical games which have realistic mixed strategy equilibria are penalty kicks in soccer, Matching Pennies and Rock-Paper-Scissors. Although these are simple two player games, they share some features with the game studied in the second paper, which has thousands of players and strategies. The second paper is written together with Colin Camerer, who generously hosted me during my stay at California Institute of Technology, as well as Joseph Tao-yi Wang and Eileen Chou. In the paper, we study the LUPI game that was introduced by the Swedish gambling monopoly in 2007. The rules of the game are simple: each person picks an integer between 1 and 99; 999 and the person that picked the lowest unique number, in other words, the lowest number that was only picked by one person, INTRODUCTION 3 wins a …xed prize. The mixed equilibrium of this game is that each player plays 1 with highest probability and attaches a lower probability the higher the number is. The idea of playing lower numbers with higher probability is intuitive, but the exact magnitude of these probabilities is not (judge for yourself by looking at Figure 1 on page 52). Although the equilibrium is both di¢ cult to compute and not particularly intuitive, players quickly learn to play close to the equilibrium prediction. To corroborate our …ndings, we also run classroom experiments in which students played the LUPI game with very similar results. What more is there to say about the LUPI game if people play according to the equilibrium prediction as if they were perfectly rational? In my opinion, a theoretical model should not only be judged by its predictions, but also by the soundness of its assumptions. The assumptions that underlie the equilibrium prediction requires a great deal in terms of both rationality and computational power and we would therefore like to have a theory with more realistic assumptions that explain how people learn to play close to the equilibrium prediction.