Explaining Games (eBook)

Boudewijn de Bruin is assistant professor of philosophy in the Faculty of Philosophy of the University of Groningen. He obtained his Ph.D. in philosophy from the Institute for Logic, Language and Computation in Amsterdam. His dissertation was awarded several prizes including a Research Prize from the Praemium Erasmianum Foundation. De Bruin did undergraduate work in musical composition at Enschede, and studied mathematics and philosophy at Amsterdam, Berkeley and Harvard. His research interests include epistemology, moral and political philosophy and philosophy of science. Receiver of several prestigious research grants, De Bruin is published widely in such journals as Ethical Theory and Moral Practice, Journal of Political Philosophy, Studies in History and Philosophy of Science and Synthese.

Contents 8
Acknowledgements 11
Introduction 13
1 Preliminaries 17
1.1 The Logic of Game Theory 17
1.1.1 Decision Theory and Game Theory 18
1.1.1.1 The Ban on Exogenous Information 18
1.1.1.2 Epistemic Characterisation Theorems 19
1.1.2 Normal Form Games 22
1.1.3 Extensive Games: The One-Shot Interpretation 27
1.1.4 Extensive Games: The Many-Moment Interpretation 30
1.1.4.1 Identity Over Time 34
1.2 A Logic for Game Theory 35
1.2.1 A Logic for Normal form Games 36
1.2.2 A Logic for Extensive Games 39
1.2.2.1 The One-Shot Interpretation 40
1.2.2.2 The Many-Moment Interpretation 41
Part I Epistemic Logic 42
2 Normal Form Games 43
2.1 The Nash Equilibrium 44
2.1.1 The Epistemic Characterisation Theorems 44
2.1.1.1 An Explicit Formalisation of Rationality 44
2.1.2 Discussion 48
2.1.2.1 The Axiom of Truth 48
2.1.2.2 The Rational Equilibration of Beliefs 50
2.1.2.3 The Ban on Exogenous Information 52
2.2 Iterated Strict Dominance 53
2.2.1 The Epistemic Characterisation Theorem 53
2.2.1.1 An Implicit, Inductive Formalisation of Rationality 54
2.2.2 Discussion 57
2.2.2.1 Axioms T and K, and the Rule of Necessitation 57
2.2.2.2 Motivation of the Axioms 59
2.2.2.3 Variants 60
2.2.2.4 More than Two Players 63
2.2.2.5 Stalnaker's Game Models Approach 64
2.3 The Dekel--Fudenberg Procedure 67
2.3.1 The Epistemic Characterisation Theorem 67
2.3.1.1 An Implicit, Inductive Formalisation of Perfect Rationality 68
2.3.2 Discussion 70
2.3.2.1 Stalnaker's Game Models Approach 70
2.3.2.2 Motivation of the Axioms 74
2.4 Mixed Iterated Strict Weak Dominance 76
2.4.1 The Epistemic Characterisation Theorem 76
2.4.2 Discussion 84
2.4.2.1 Comparison with the Literature 85
2.4.2.2 Motivation of the Axioms 86
2.4.2.3 The Ban on Exogenous Information 89
3 Extensive Games 91
3.1 The One-Shot Interpretation 92
3.1.1 The Epistemic Characterisation Result 92
3.1.1.1 An Explicit Formalisation of Rationality 94
3.1.1.2 An Implicit, Inductive Formalisation of Rationality 96
3.1.2 Discussion 99
3.2 The Many-Moment Interpretation 100
3.2.1 The Inconsistency Result 100
3.2.1.1 An Explicit Formalisation of Rationality 102
3.2.2 Discussion 106
Part II Epistemology 109
4 Applications of Game Theory 110
4.1 Logical Form 111
4.1.1 Rationality 111
4.1.1.1 Max Weber and John Stuart Mill 112
4.1.1.2 Decision and Game Theory 114
4.1.2 Decision Theory 116
4.1.2.1 Explanatory Use 116
4.1.2.2 Normative Use 119
4.1.3 Game Theory 122
4.1.3.1 Explanatory Use 122
4.1.3.2 Normative Use 124
4.2 Game Theory as an Explanatory Theory 126
4.2.1 The Reduction 126
4.2.2 The Ban on Exogenous Information 127
4.2.2.1 A Narrow Epistemology 127
4.2.2.2 The Correlated Equilibrium 129
4.3 Game Theory as a Normative Theory 132
4.3.1 Collective Advice 132
4.3.2 Individual Advice 133
4.3.2.1 Actuality 134
4.3.2.2 Probability 135
4.3.2.3 Possibility 135
5 The Methodology of Game Theory 137
5.1 Truth in the Abstract 140
5.1.1 The Methodology 140
5.1.1.1 John Stuart Mill 140
5.1.1.2 Robert Aumann and Ariel Rubinstein 141
5.1.2 The Research Habits 143
5.1.2.1 Overmathematisation 144
5.1.2.2 Introversion 144
5.1.2.3 Model-Tinkering 145
5.2 A Case Study: Refining the Nash Equilibrium 146
5.2.1 The Nash Equilibrium Refinement Programme 147
5.2.1.1 The Nash Equilibrium 147
5.2.1.2 The Subgame-Perfect Equilibrium 149
5.2.1.3 The Perfect Equilibrium 151
5.2.1.4 The Proper Equilibrium 153
5.2.2 Mathematics-Driven Mathematisation in the Nash Equilibrium Refinement Programme 154
5.2.3 Application-Driven Mathematisation in the Epistemic Programme 159
Conclusion 162
A Notation, Definitions, Theorems 166
A.1 Decision Theory 166
A.2 Normal Form Games 167
A.3 Extensive Games 168
Bibliography 170
Index 177