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