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

Herbert Gintis
Princeton University Press
Publication Date: 
Number of Pages: 
[Reviewed by
William J. Satzer
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Game theory, according to the author, is an indispensable tool for modeling human behavior. He believes that behavioral disciplines that reject game theory or regard it as peripheral are handicapped theoretically. (“Behavioral disciplines” here include psychology, economics, anthropology, sociology, political science and some aspects of biology.) At the same time, the author notes, many champions of game theory make extravagant claims about it; indeed, some think it capable of explaining all aspects of human social existence.

Throughout the book the author attempts to put game theory in perspective for the behavioral sciences. One of his main contributions here is to point out that the Nash equilibrium, the traditional equilibrium concept of game theory, is achieved by rational actors only when they share beliefs about how the game is to be played. He proposes instead the concept of a correlated equilibrium wherein the correlating devices can be broadly identified with social norms. The author contends that game theory in the social sciences needs a broader social theory behind it.

The author is an economist and an advocate of evolutionary game theory, which – he believes – can remedy many of the weaknesses of traditional game theory. His Game Theory Evolving is a companion volume to the book of this review. There is a fair amount of mathematics in the current book, and it ranges from the analysis of special games to axiom systems and a symbolic description of properties of a knowledge operator in modal logic. I did find the following comment from the author’s preface rather troubling:

Game theory can be used very profitably by researchers who do not know or care about mathematical intricacies but rather treat mathematics as but one of many tools deployed in the search for truth. I assert then that my arguments are correct and logically argued. I will leave rigor to the mathematicians.

(Would the author claim similar infallibility for his non-mathematical arguments?) It is especially bothersome because there are enough typographical errors throughout the mathematical sections to make some of the author’s arguments incomprehensible. It is difficult even to make sense of some of the expressions because they are so scrambled. In other places, arguments are so abbreviated — and at times, unsupported — that they’re very hard to follow. Given that, I have to wonder what the mathematical portions of the book were meant to do, how they might serve its readers, and indeed just who the intended readers might be.

The strengths of the book are in the author’s command of the scope of game theory across the behavioral sciences and in his assessment of the needs for modifications to the way game theory is applied in those disciplines. The value of the book to a mathematical reader is that broad perspective of how game theory is applied in the behavioral sciences.

Bill Satzer ( is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.


Preface xiii

Chapter 1: Decision Theory and Human Behavior 1
1.1 Beliefs, Preferences, and Constraints 4
1.2 The Meaning of Rational Action 6
1.3 Why Are Preferences Consistent? 7
1.4 Time Inconsistency 8
1.5 Bayesian Rationality and Subjective Priors 11
1.6 The Biological Basis for Expected Utility 16
1.7 The Allais and Ellsberg Paradoxes 16
1.8 Risk and the Shape of the Utility Function 18
1.9 Prospect Theory 21
1.10 Heuristics and Biases in Decision Making 26

Chapter 2: Game Theory: Basic Concepts 30
2.1 The Extensive Form 30
2.2 The Normal Form 33
2.3 Mixed Strategies 34
2.4 Nash Equilibrium 35
2.5 The Fundamental Theorem of Game Theory 36
2.6 Solving for Mixed-Strategy Nash Equilibria 37
2.7 Throwing Fingers 38
2.8 The Battle of the Sexes 38
2.9 The Hawk-Dove Game 39
2.10 The Prisoner's Dilemma 40
2.11 Alice, Bob, and the Choreographer 41
2.12 An Efficiency-Enhancing Choreographer 43
2.13 The Correlated Equilibrium Solution Concept 44

Chapter 3: Game Theory and Human Behavior 45
3.1 Self- and Other-Regarding Preferences 46
3.2 Methodological Issues in Behavioral Game Theory 49
3.3 An Anonymous Market Exchange 52
3.4 The Rationality of Altruistic Giving 54
3.5 Conditional Altruistic Cooperation 56
3.6 Altruistic Punishment 57
3.7 Strong Reciprocity in the Labor Market 59
3.8 Altruistic Third-Party Punishment 61
3.9 Altruism and Cooperation in Groups 64
3.10 Inequality Aversion 68
3.11 The Trust Game 71
3.12 Character Virtues 73
3.13 The Situational Character of Preferences 75
3.14 The Dark Side of Altruistic Cooperation 77
3.15 Norms of Cooperation: Cross-Cultural Variation 78

Chapter 4: Rationalizability and Common Knowledge of Rationality 83
4.1 Epistemic Games 83
4.2 A Simple Epistemic Game 86
4.3 An Epistemic Battle of the Sexes 87
4.4 Dominated and Iteratedly Dominated Strategies 88
4.5 Eliminating Weakly Dominated Strategies 89
4.6 Rationalizable Strategies 90
4.7 Eliminating Strongly Dominated Strategies 92
4.8 Common Knowledge of Rationality 93
4.9 Rationalizability and Common Knowledge of Rationality 94
4.10 The Beauty Contest 94
4.11 The Traveler's Dilemma 95
4.12 The Modified Traveler's Dilemma 96
4.13 Global Games 98
4.14 CKR Is an Event, Not a Premise 100

Chapter 5: Extensive Form Rationalizability 102
5.1 Backward Induction and Dominated Strategies 102
5.2 Subgame Perfection 104
5.3 Subgame Perfection and Incredible Threats 105
5.4 The Surprise Examination 105
5.5 The Common Knowledge of Logicality Paradox 106
5.6 The Repeated Prisoner's Dilemma 107
5.7 The Centipede Game 108
5.8 CKR Fails Off the Backward Induction Path 110
5.9 How to Play the Repeated Prisoner's Dilemma 112
5.10 The Modal Logic of Knowledge 114
5.11 Backward Induction and Extensive Form CKR 115
5.12 Rationality and Extensive Form CKR 118
5.13 On the Nonexistence of CKR 119

Chapter 6: The Mixing Problem: Purification and Conjectures 121
6.1 Why Play Mixed Strategies? 121
6.2 Harsanyi's Purification Theorem 123
6.3 A Reputational Model of Honesty and Corruption 125
6.4 Purifying Honesty and Corruption 128
6.5 Epistemic Games: Mixed Strategies as Conjectures 128
6.6 Resurrecting the Conjecture Approach to Purification 129

Chapter 7: Bayesian Rationality and Social Epistemology 132
7.1 The Sexes: From Battle to Ballet 133
7.2 The Choreographer Trumps Backward Induction 134
7.3 Property Rights and Correlated Equilibrium 135
7.4 Convention as Correlated Equilibrium 136
7.5 Correlated Strategies and Correlated Equilibria 136
7.6 Correlated Equilibrium and Bayesian Rationality 138
7.7 The Social Epistemology of Common Priors 139
7.8 The Social Epistemology of Common Knowledge 141
7.9 Social Norms 143
7.10 Game Theory and the Evolution of Norms 143
7.11 The Merchants' Wares 144

Chapter 8: Common Knowledge and Nash Equilibrium 146
8.1 Conditions for a Nash Equilibrium in Two-Player Games 146
8.2 A Three-Player Counterexample 147
8.3 The Modal Logic of Common Knowledge 149
8.4 The Commonality of Knowledge 152
8.5 The Tactful Ladies 153
8.6 The Tactful Ladies and the Commonality of Knowledge 156
8.7 Agreeing to Disagree 158
8.8 The Demise of Methodological Individualism 161

Chapter 9: Reflective Reason and Equilibrium Refinements 164
9.1 Perfect, Perfect Bayesian, and Sequential Equilibria 166
9.2 Incredible Threats 167
9.3 Unreasonable Perfect Bayesian Equilibria 170
9.4 The LBR criterion picks out the sequential equilibrium 171
9.5 Selten's Horse: Sequentiality vs. the LBR criterion 171
9.6 The Spence Signaling Model 173
9.7 Irrelevant Node Additions 174
9.8 Improper Sequential Equilibria 175
9.9 Second-Order Forward Induction 176
9.10 Beer and Quiche Without the Intuitive Criterion 177
9.11 An Unreasonable Perfect Equilibrium 178
9.12 The Principle of Insufficient Reason 179
9.13 The Principle of Honest Communication 179
9.14 Induction: Forward is Robust, Backward is Fragile 180

Chapter 10: The Analytics of Human Sociality 181
10.1 Explaining Cooperation: An Overview 181
10.2 Bob and Alice Redux 183
10.3 The Folk Theorem 185
10.4 The Folk Theorem with Imperfect Public Information 188
10.5 Cooperation with Private Signaling 193
10.6 One Cheer For the Folk Theorem 195
10.7 Altruistic Punishing in the Public Goods Game 197
10.8 The Failure of Models of Self-Regarding Cooperation 200

Chapter 11: The Evolution of Property Rights 201
11.1 The Endowment Effect 201
11.2 Territoriality 204
11.3 Property Rights in Young Children 207
11.4 Respect for Possession in Nonhuman Animals 207
11.5 Conditions for a Property Equilibrium 210
11.6 Property and Antiproperty Equilibria 213
11.7 An Antiproperty Equilibrium 217
11.8 Property Rights as Choreographer 220

Chapter 12: The Unification of the Behavioral Sciences 221
12.1 Gene-Culture Coevolution: The Biological Model 223
12.2 Culture and Physiology of Human Communication 228
12.3 Biological and Cultural Dynamics 229
12.4 The Theory of Norms: The Sociological Model 231
12.5 Socialization and the Internalization of Norms 233
12.6 Rational Choice: The Economic Model 234
12.7 Deliberative Choice: The Psychological Model 236
12.8 Application: Addictive Behavior 238
12.9 Game Theory: The Universal Lexicon of Life 239
12.10 Epistemic Game Theory and Social Norms 240
12.11 Society as a Complex Adaptive System 242
12.12 Counterpoint: Biology 244
12.13 Counterpoint: Economics 245
12.14 Counterpoint: Psychology 245
12.15 The Behavioral Disciplines Can Be Unified 247

Chapter 13: Summary 248
Chapter 14: Table of Symbols 250
References 253
Index 283