ISBN: 3540414061
TITLE: Focal Points in Framed Games
AUTHOR: Andr Casajus
TOC:

1 Introduction 1
1.1 Static Focal Points 1
1.1.1 Coordination 1
1.1.2 Bargaining 4
1.2 Dynamic Focal Points 6
1.3 Outline 7
2. Static Focal Points in Framed Strategic Games 9
2.1 Introduction 9
2.2 Examples 10
2.3 Harsanyi and Selten's Symmetry Invariance Requirement 13
2.3.1 Introduction 13
2.3.2 Strategic Games 14
2.3.3 Solution Concepts 15
2.3.4 Invariance with Respect to Isomorphisms 16
2.3.5 Symmetry Invariance 19
2.4 Rationalizing Static Focal Points 24
2.4.1 Rationalizing the Choice of a Salient Option 24
2.4.2 The Variable Frame Theory of Focal Points 26
2.4.3 Sugden's Labelling 34
2.4.4 The Principle of Coordination 36
2.5 Framed Strategic Games (FSGs) 38
2.5.1 Frames 38
2.5.2 Language Invariance 41
2.5.3 Symmetry Invariance 43
2.5.4 Meaning and Structure of Labels - an Extraterrestrial's Perspective 45
2.5.5 Separating FSGs 46
2.5.6 Applications 48
2.6 Focal Points in FSG Representations of VUMGs 51
2.6.1 FSG Representations of VUMGs 52
2.6.2 An Example 52
2.6.3 Reduction of FSGs and Focal Points in VUMGs 53
3. Weak Isomorphisms of Extensive Games 55
3.1 Introduction 55
3.2 Finite Extensive Games with Perfect Recall 58
3.2.1 Definition 58
3.2.2 Perfect Recall 61
3.2.3 Strategies 63
3.2.4 Subgames 64
3.2.5 Solution Concepts 65
3.3 Invariance with Respect to Weak Isomorphisms 67
3.3.1 Weak Isomorphisms of Extensive Games 67
3.3.2 Weak Isomorphism Invariance 73
3.3.3 Weak Symmetry Invariance 74
3.3.4 The Order of Actions 75
3.4 Strong Isomorphisms of Extensive Games 83
3.5 Traditional Extensive Representations of Strategic Games 86
3.5.1 Definition 86
3.5.2 Symmetry in Traditional Representations of Strategic Games 87
3.6 Conclusion 89
4. Dynamic Focal Points in Framed Extensive Games 91
4.1 Introduction 91
4.2 Examples 93
4.2.1 Crawford & Haller's Rule for Repeated Matching Games 93
4.2.2 Conscious Production of a Description 94
4.3 Modelling Dynamic Focal Points 95
4.3.1 Extensive Games 95
4.3.2 Extensive Games with History 97
4.3.3 Framed Strategic Games - Ad hoc Approach 100
4.3.4 Framed Strategic Games - General Approach 101
4.4 Framed Extensive Games (FEGs) 107
4.4.1 Frames 107
4.4.2 Weak Isomorphisms of FEGs and Language Invariance 108
4.4.3 Weak Symmetries of FEGs 109
4.5 Modelling Dynamic Focal Points by FEGs 109
4.5.1 Crawford & Haller's Rule 109
4.5.2 Conscious Production of a Description 111
4.5.3 History Labelled Agent Normal Forms 112
5. Conclusion 115
5.1 Static Focal Points in Framed Strategic Games 115
5.2 Weak Isomorphisms of Extensive Games 116
5.3 Dynamic Focal Points in Framed Extensive Games 118
5.4 Perspective 118
List of Symbols and Abbreviations 121
List of Figures 127
Bibliography 129
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