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El. knyga: Language Of Game Theory, The: Putting Epistemics Into The Mathematics Of Games

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(New York Univ, Usa)
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This volume contains eight papers written by Adam Brandenburger and his co-authors over a period of 25 years. These papers are part of a program to reconstruct game theory in order to make what players believe about a game a central feature of the theory. The program — now called epistemic game theory — extends the classical definition of a game model to include not only the game matrix or game tree, but also what each player believes about how the game will be played, and even higher-order beliefs. With this richer mathematical framework, it becomes possible to determine what different configurations of beliefs among the players imply for how a game is played. Epistemic game theory includes traditional equilibrium-based theory as a special case, but allows for a wide range of non-equilibrium behavior.
Foreword ix
About the Author xv
Acknowledgments xvii
Introduction xix
Chapter 1 An Impossibility Theorem on Beliefs in Games
1(30)
Adam Brandenburger
H. Jerome Keisler
1 Introduction
2(3)
2 The Existence Problem for Complete Belief Models
5(1)
3 Belief Models
6(2)
4 Complete Belief Models
8(2)
5 Impossibility Results
10(3)
6 Assumption in Modal Logic
13(2)
7 Impossibility Results in Modal Form
15(4)
8 Strategic Belief Models
19(2)
9 Weakly Complete and Semi-Complete Models
21(3)
10 Positively and Topologically Complete Models
24(3)
11 Other Models in Game Theory
27(4)
References
29(2)
Chapter 2 Hierarchies of Beliefs and Common Knowledge
31(12)
Adam Brandenburger
Eddie Dekel
1 Introduction
31(2)
2 Construction of Types
33(3)
3 Relationship to the Standard Model of Differential Information
36(7)
References
40(3)
Chapter 3 Rationalizability and Correlated Equilibria
43(16)
Adam Brandenburger
Eddie Dekel
1 Introduction
43(3)
2 Correlated Rationalizability and A Posteriori Equilibria
46(5)
3 Independent Rationalizability and Conditionally Independent A Posteriori Equilibria
51(3)
4 Objective Solution Concepts
54(5)
References
56(3)
Chapter 4 Intrinsic Correlation in Games
59(54)
Adam Brandenburger
Amanda Friedenberg
1 Introduction
60(2)
2 Intrinsic vs. Extrinsic Correlation
62(1)
3 Comparison
63(3)
4 Organization of the
Chapter
66(1)
5 Type Structures
66(3)
6 The Main Result
69(4)
7 Comparison Contd
73(3)
8 Formal Presentation
76(1)
9 CI and SUFF Formalized
77(2)
10 RCBR Formalized
79(1)
11 Main Result Formalized
80(7)
12 Conclusion
87(26)
Appendices
88(22)
References
110(3)
Chapter 5 Epistemic Conditions for Nash Equilibrium
113(24)
Robert Aumann
Adam Brandenburger
1 Introduction
113(4)
2 Interactive Belief Systems
117(3)
3 An Illustration
120(1)
4 Formal Statements and Proofs of the Results
121(3)
5 Tightness of the Results
124(4)
6 General (Infinite) Belief Systems
128(1)
7 Discussion
129(8)
References
135(2)
Chapter 6 Lexicographic Probabilities and Choice Under Uncertainty
137(24)
Lawrence Blume
Adam Brandenburger
Eddie Dekel
1 Introduction
138(2)
2 Subjective Expected Utility on Finite State Spaces
140(2)
3 Lexicographic Probability Systems and Non-Archimedean SEU Theory
142(3)
4 Admissibility and Conditional Probabilities
145(2)
5 Lexicographic Conditional Probability Systems
147(3)
6 A "Numerical" Representation for Non-Archimedean SEU
150(2)
7 Stochastic Independence and Product Measures
152(9)
Appendix
154(5)
References
159(2)
Chapter 7 Admissibility in Games
161(52)
Adam Brandenburger
Amanda Friedenberg
H. Jerome Keisler
1 Introduction
162(1)
2 Heuristic Treatment
163(13)
3 SAS's and the IA Set
176(1)
4 Lexicographic Probability Systems
177(1)
5 Assumption
178(2)
6 Properties of Assumption
180(1)
7 Type Structures
181(4)
8 Characterization of RCAR
185(2)
9 Characterization of RmAR in a Complete Structure
187(3)
10 A Negative Result
190(1)
11 Discussion
190(23)
Appendices
192(18)
References
210(3)
Chapter 8 Self-Admissible Sets
213(38)
Adam Brandenburger
Amanda Friedenberg
1 Introduction
213(3)
2 Preview
216(1)
3 Self-Admissible Sets
217(3)
4 Applications
220(4)
5 Strategic-Form Properties of SAS's
224(1)
6 Extensive-Form Properties of SAS's
225(4)
7 Perfect-Information Games
229(6)
8 Discussion
235(16)
Appendix
240(7)
References
247(4)
Subject Index 251(10)
Author Index 261
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