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