The Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences

305 Pages·2009·2.31 MB·English

by  Herbert Gintis

The Bounds of Reason
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The Bounds of Reason
Game Theory and the Unification
of the Behavioral Sciences
Herbert Gintis
PrincetonUniversityPress
PrincetonandOxford
Copyright(cid:2)c 2009byPrincetonUniversity Press
Published by PrincetonUniversity Press, 41WilliamStreet,Princeton, NewJersey08540
In the United Kingdom: PrincetonUniversity Press, 6OxfordStreet, Woodstock, Oxfordshire
OX201TW
AllRights Reserved
Library ofCongressCataloging-in-Publication Data
Gintis, Herbert
The Bounds of Reason: GameTheory and the Unificationof theBehavioralSciences/
HerbertGintis
p. cm.
Includes bibliographicalreferencesand index.
ISBN 978-0-691-14052-0(hardcover: alk. paper)1. Gametheory. 2. Practicalreason.
3. Human behavior. 4. Socialsciences–Methodology. 5. Psychology. I. Title.
HB144.G552009
519.3–dc22
2008036522
British Library Cataloging-in-Publication Data is available
The publisher wouldliketo acknowledgethe author ofthis volumefor providingthe
camera-readycopyfromwhichthis bookwas printed
This book has beencomposedin Timesand Mathtime by theauthor
Printed onacid-freepaper.
press.princeton.edu
Printed inthe United States of America
10987654 321
This book is dedicated to Morris and Henrietta
Malena,GersonGintis,andFloraandMelvinGreisler.
Wegetalongwithoutyouverywell.Ofcoursewedo.
There is no sorrow so great that it
doesnotfinditsbackgroundinjoy.
NielsBohr
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Contents
Preface xiii
1 DecisionTheory andHumanBehavior 1
1.1 Beliefs, Preferences, andConstraints 4
1.2 The Meaning ofRationalAction 6
1.3 WhyAre PreferencesConsistent? 7
1.4 Time Inconsistency 8
1.5 Bayesian Rationalityand SubjectivePriors 11
1.6 The BiologicalBasis forExpected Utility 16
1.7 The Allais andEllsberg Paradoxes 16
1.8 Risk and theShapeoftheUtilityFunction 18
1.9 ProspectTheory 21
1.10 Heuristics andBiases inDecision Making 26
2 Game Theory: Basic Concepts 30
2.1 The Extensive Form 30
2.2 The NormalForm 33
2.3 Mixed Strategies 34
2.4 Nash Equilibrium 35
2.5 The FundamentalTheoremofGame Theory 36
2.6 SolvingforMixed-StrategyNash Equilibria 37
2.7 ThrowingFingers 38
2.8 The Battle oftheSexes 38
2.9 The Hawk-Dove Game 39
2.10 The Prisoner’sDilemma 40
2.11 Alice, Bob, and theChoreographer 41
2.12 An Efficiency-EnhancingChoreographer 43
2.13 The CorrelatedEquilibriumSolutionConcept 44
3 Game TheoryandHumanBehavior 45
3.1Self-andOther-RegardingPreferences46
viii Contents
3.2 MethodologicalIssues inBehavioralGameTheory 49
3.3 An AnonymousMarketExchange 52
3.4 The RationalityofAltruisticGiving 54
3.5 ConditionalAltruisticCooperation 56
3.6 AltruisticPunishment 57
3.7 StrongReciprocityintheLabor Market 59
3.8 AltruisticThird-PartyPunishment 61
3.9 AltruismandCooperationinGroups 64
3.10 InequalityAversion 68
3.11 The Trust Game 71
3.12 Character Virtues 73
3.13 The SituationalCharacterofPreferences 75
3.14 The DarkSideofAltruisticCooperation 77
3.15 NormsofCooperation: Cross-CulturalVariation 78
4 RationalizabilityandCommon KnowledgeofRationality 83
4.1 Epistemic Games 83
4.2 A SimpleEpistemic Game 86
4.3 An EpistemicBattle oftheSexes 87
4.4 Dominatedand IteratedlyDominatedStrategies 88
4.5 EliminatingWeakly DominatedStrategies 89
4.6 Rationalizable Strategies 90
4.7 EliminatingStronglyDominatedStrategies 92
4.8 CommonKnowledgeofRationality 93
4.9 RationalizabilityandCommonKnowledgeofRationality 94
4.10 The Beauty Contest 94
4.11 The Traveler’s Dilemma 95
4.12 The ModifiedTraveler’s Dilemma 96
4.13 GlobalGames 98
4.14 CKR Is anEvent, NotaPremise 100
5 ExtensiveForm Rationalizability 102
5.1 BackwardInductionandDominatedStrategies 102
5.2 SubgamePerfection 104
5.3 SubgamePerfectionand IncredibleThreats 105
5.4 The SurpriseExamination 105
5.5 The CommonKnowledgeofLogicalityParadox 106
5.6 The Repeated Prisoner’sDilemma 107
Contents ix
5.7 The Centipede Game 108
5.8 CKR Fails Offthe BackwardInductionPath 110
5.9 Howto PlaytheRepeated Prisoner’sDilemma 112
5.10 The Modal Logic ofKnowledge 114
5.11 BackwardInductionandExtensive FormCKR 115
5.12 Rationalityand Extensive FormCKR 118
5.13 On theNonexistence ofCKR 119
6 The MixingProblem: PurificationandConjectures 121
6.1 WhyPlay MixedStrategies? 121
6.2 Harsanyi’s PurificationTheorem 123
6.3 A ReputationalModelofHonesty andCorruption 125
6.4 PurifyingHonesty andCorruption 128
6.5 Epistemic Games: Mixed Strategiesas Conjectures 128
6.6 Resurrectingthe ConjectureApproachtoPurification 129
7 BayesianRationalityandSocialEpistemology 132
7.1 The Sexes: FromBattletoBallet 133
7.2 The ChoreographerTrumpsBackwardInduction 134
7.3 PropertyRights andCorrelatedEquilibrium 135
7.4 Convention as CorrelatedEquilibrium 136
7.5 CorrelatedStrategiesand CorrelatedEquilibria 136
7.6 CorrelatedEquilibriumand Bayesian Rationality 138
7.7 The SocialEpistemology ofCommonPriors 139
7.8 The SocialEpistemology ofCommonKnowledge 141
7.9 SocialNorms 143
7.10 Game Theoryand theEvolutionofNorms 143
7.11 The Merchants’ Wares 144
8 Common KnowledgeandNashEquilibrium 146
8.1 ConditionsforaNashEquilibriuminTwo-PlayerGames146
8.2 A Three-PlayerCounterexample 147
8.3 The Modal Logic ofCommonKnowledge 149
8.4 The CommonalityofKnowledge 152
8.5 The Tactful Ladies 153
8.6 The Tactful Ladies andthe CommonalityofKnowledge 156
8.7 AgreeingtoDisagree 158
8.8 The Demise ofMethodologicalIndividualism 161