
The Bounds of Reason: Game Theory for the Behavioral Sciences The Bounds of Reason: Game Theory for the Behavioral Sciences Herbert Gintis Princeton University Press Princeton, New Jersey Copyright c 2008 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 3 Market Place, Woodstock, Oxfordshire OX20 1SY All Rights Reserved Library of Congress Cataloging-in-Publication Data Gintis, Herbert The Bounds of Reason Herbert Gintis p. cm. Includes bibliographical references and index. ISBN 0-691-00942-2 (cloth: alk. paper)—ISBN 0-691-00943-0 (pbk.: alk. paper) 1. Game theory. 2. Economics, Mathematical. I. Title. HB144.G562008 330’.01’5193–dc21 99-054923 This book has been composed in Times and Mathtime by the author The paper used in this publication meets the minimum requirements of ANSI/NISO Z39.48- 1992 (R1997) (Permanence of Paper) www.pup.princeton.edu Printed in the United States of America 10987654321 10987654321 (pbk.) This book is dedicated to Shirley and Gerson Gintis, and Flora and Melvin Greisler, with all my love. There is no sorrow so great that it does not find its background in joy. Neils Bohr Contents Preface xii 1 Decision Theory and Human Behavior 2 1.1 Beliefs, Preferences, and Constraints 6 1.2 TheMeaningofRationalAction 7 1.3 Why Are Preferences Consistent? 9 1.4 TimeInconsistency 10 1.5 TheExpectedUtilityPrinciple 14 1.6 TheBiologicalBasisforExpectedUtility 18 1.7 The Allais and Ellsberg Paradoxes 18 1.8 RiskandtheShapeoftheUtilityFunction 21 1.9 Prospect Theory 24 1.10 HeuristicsandBiasesinDecision-making 29 2 Game Theory: Basic Concepts 33 2.1 BigJohnandLittleJohn 33 2.2 The Extensive Form 39 2.3 TheNormalForm 42 2.4 Mixed Strategies 43 2.5 NashEquilibrium 43 2.6 TheFundamentalTheoremofGameTheory 44 2.7 SolvingforMixedStrategyNashEquilibria 45 2.8 ThrowingFingers 46 2.9 BattleoftheSexes 47 2.10 TheHawk-DoveGame 49 2.11 ThePrisoner’sDilemma 49 3 Game Theory and Human Behavior 51 3.1 MethodologicalIssues inBehavioralGameTheory 55 3.2 AnAnonymousMarketExchange 59 3.3 TheRationalityofAltruisticGiving 61 viii Contents 3.4 ConditionalAltruisticCooperation 62 3.5 AltruisticPunishment 64 3.6 StrongReciprocityintheLaborMarket 65 3.7 AltruisticThirdPartyPunishment 68 3.8 AltruismandCooperationinGroups 71 3.9 InequalityAversion 74 3.10 The Trust Game 77 3.11 Character Virtues 79 3.12 TheExternalValidityofLaboratoryExperiments 81 4 Eliminating Dominated Strategies 86 4.1 BackwardInductionandSubgamePerfection 88 4.2 ExperimentalEvidenceonBackwardInduction 90 4.3 The Repeated Prisoner’s Dilemma 92 4.4 Reciprocators 92 4.5 RationalizabilityandDominatedStrategies 94 4.6 TheCentipedeGame 96 4.7 RationalizabilityintheCentipedeGame 98 4.8 The Traveler’s Dilemma 98 4.9 AWeaknessoftheRationalizabilityCriterion 99 5 The Incoherence of Backward Induction 102 5.1 TheInternalInconsistencyofBackwardInduction 102 5.2 HowtoPlaytheCentipedeGame 104 5.3 TheSurpriseExamination 106 5.4 DominatedStrategiesintheExtensiveForm 106 5.5 The Chain Store Paradox Resolved 107 5.6 CautiousRationalizability 107 5.7 ExamplesofCautiousRationalizability 109 6 The Mixing Problem 110 6.1 Harsanyi’sPurificationTheorem 112 6.2 Epistemic Games: Mixed Strategies as Conjectures 114 6.3 Resurrecting the Conjecture Approach to Purification 117 7 Bayesian Rationality and Social Epistemology 119 7.1 Introduction 119 7.2 Alice,Bob,andtheChoreographer 120 Contents ix 7.3 AnEfficiency-enhancingChoreographer 121 7.4 CorrelatedStrategiesandCorrelatedEquilibria 122 7.5 TheGeometricStructureofCorrelatedEquilibria 124 7.6 CorrelatedEquilibriumandBayesianRationality 126 7.7 WhyPlayaCorrelatedEquilibrium? 126 7.8 SocialEpistemology 127 7.9 SocialNorms 130 7.10 GameTheoryandtheEvolutionofNorms 130 7.11 The Merchants’ Wares 131 7.12 TheCharacterofSocialNorms 132 7.13 Common Priors 133 8 Epistemic Game Theory 136 8.1 TheModalLogicofKnowledge 137 8.2 BackwardInductionandRationality 140 8.3 Conditions for Nash Equilibrium in Two-Player Games 142 8.4 AThree-playerCounterexample 144 8.5 CounterexampleII 145 8.6 TheModalLogicofCommonKnowledge 147 8.7 TheCommonalityofKnowledge 150 8.8 The Tactful Ladies 151 8.9 The Tactful Ladies and the Commonality of Knowledge 154 8.10 AgreeingtoDisagree 155 8.11 TheDemiseofMethodologicalIndividualism 158 9 Reflective Reason and Equilibrium Refinements 160 9.1 IncredibleThreatsandTremblingHands 162 9.2 The Local Best Response Criterion 163 9.3 AForwardInductionEquilibrium 164 9.4 Selten’s Horse 166 9.5 TheSpenceSignalingModel 167 9.6 The LBR CriterionIgnoresIrrelevantNode Changes 169 9.7 TheLBRCriterioninaMoneyBurningGame 170 9.8 BeerandQuichewithouttheIntuitiveCriterion 171 9.9 ThePrincipleofInsufficientReason 172 10 The Analytics of Human Sociality 174 10.1 ExplainingCooperation:AnOverview 174 x Contents 10.2 BobandAliceRedux 177 10.3 TheFolkTheorem 179 10.4 The Folk Theorem with Imperfect Public Information 182 10.5 CooperationwithPrivateSignaling 188 10.6 PurificationwithPrivateInformation 189 10.7 AReputationalModelofHonestyandCorruption 190 10.8 HonestyandCorruptionII 192 10.9 AltruisticPunishinginthePublicGoodsGame 193 References 199 Preface The eternal mystery of the world is its comprehensibility. Albert Einstein Mathematics without natural history is sterile, but natural history without mathematics is muddled. John Maynard Smith Game theory is central to understanding the dynamics of life forms in general, and humans in particular. Living creatures not only play games, but dynamically transform the games they play, and have themselves thereby evolved their unique identities. For this reason, the material in this book is foundational to all the behavioral sciences, from biology, psychology and economics to anthropology, sociology, and political science. We humans have a completely stunning capacity to reason, and to apply the fruits of reason to the transformation of our social existence. Social interactions in a vast array of species can be analyzed with game theory, yet only humans are capable of playing a game after being told its rules. This book is based on the appreciation that evolution and reason interact in constituting the social life and strategic interaction of humans. Game theory, however, is not everything. This book systematically and single-mindedly denies one of the guiding prejudices of contemporary game theory. This is the notion that game theory and the implications of Bayesian rationality (developed in chapter 1) are sufficient, at least insofar as human beings are rational, to explain all of human social existence. In fact, game theory is complementary to ideas developed and championed in all the be- havioral disciplines. Behavioral scientists who have rejected game theory in reaction to the extravagant claims of some of its adherents may thus want to reconsider their position, recognizing the fact that, just as game theory without broader social theory is merely technical bravado, so social theory without game theory is a fatally handicapped enterprise. The bounds of reason are not irrationality, but sociality. As we stress throughout this book, the assumption that humans engaged in strategic in- teraction are rational is an excellent and indispensable first (and perhaps even second and third) approximation. However, humans have what we may called a social epistemology, meaning that we have reasoning pro- cesses that afford us forms of knowledge and understanding, especially un- derstanding of the content of other minds, that are unavailable to merely “rational” creatures. It is these epistemological features that characterize our species, and bid us to develop epistemic game theory in the pages that follow. That game theory does not stand alone entails denying methodological individualism, a philosophical position asserting that all social phenomena can be explained purely in terms of the characteristics of rational agents, the actions available to them, and the constraints that they face. This position is incorrect because, as we shall see, human society is a system with emer- gent properties, including social norms, that cannot be derived as product of interacting rational agents, any more than the chemical and biological prop- erties of matter can be derived from the behavior of fundamental particles. Moreover, humans have a social epistemology—evolved cognitive capaci- ties that permit the sharing of beliefs across agents in a manner completely opaque to classical and even standard epistemic game theory. Evolutionary game theory often succeeds where classical game theory fails (Gintis 2009). The evolutionary approach to strategic interaction helps us understand the emergence, transformation, and stabilization of behav- iors. In evolutionary game theory, successful strategies diffuse across pop- ulations of players rather than being learned inductively by disembodied rational agents. Moreover, reasoning is costly, so rational agents will not often even attempt to learn optimal strategies to complicated games, but rather will copy the behavior of successful agents whom they encounter. Evolutionary game theory allows us to investigate the interaction of learn- ing, mutation, and imitation in the spread of strategies when information processing is costly. But, evolutionary game theory cannot deal with unique events, such as strangers interacting in a novel environment, or Middle East peace nego- tiations. Moreover, by assuming that agents have very low level cognitive capacities, evolutionary game theory
Details
-
File Typepdf
-
Upload Time-
-
Content LanguagesEnglish
-
Upload UserAnonymous/Not logged-in
-
File Pages213 Page
-
File Size-