| Description |
1 online resource (xxxiv, 263 pages) : illustrations |
| Series |
World Scientific Series in Economic Theory |
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World Scientific series in economic theory ; v. 5
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| Contents |
Foreword; Contents; About the Author; Acknowledgments; Introduction; Epistemic Game Theory; Theory or Language?; Limits in Principle; Fundamental Theorem of Epistemic Game Theory; Epistemic vs. Ontic Views; Invariance and Admissibility; Questions and Directions; References; Chapter 1. An Impossibility Theorem on Beliefs in Games; 1 Introduction; 2 The Existence Problem for Complete Belief Models; 3 Belief Models; 4 Complete Belief Models; 5 Impossibility Results; 6 Assumption in Modal Logic; 7 Impossibility Results in Modal Form; 8 Strategic Belief Models |
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9 Weakly Complete and Semi-Complete Models10 Positively and Topologically Complete Models; 11 Other Models in Game Theory; References; Chapter 2. Hierarchies of Beliefs and Common Knowledge; 1 Introduction; 2 Construction of Types; 3 Relationship to the Standard Model of Differential Information; References; Chapter 3. Rationalizability and Correlated Equilibria; 1 Introduction; 2 Correlated Rationalizability and A Posteriori Equilibria; 3 Independent Rationalizability and Conditionally Independent A Posteriori Equilibria; 4 Objective Solution Concepts; References |
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Chapter 4. Intrinsic Correlation in Games1 Introduction; 2 Intrinsic vs. Extrinsic Correlation; 3 Comparison; 4 Organization of the Chapter; 5 Type Structures; 6 The Main Result; 7 Comparison Contd.; 8 Formal Presentation; 9 CI and SUFF Formalized; 10 RCBR Formalized; 11 Main Result Formalized; 12 Conclusion; Appendices; Appendix A. CI and SUFF Contd.; Appendix B. Proofs for Section 8; Appendix C. Proofs for Section 9; Appendix D. Proofs for Section 10; Appendix E. Proofs for Section 11; Appendix F.A Finite-Levels Result; Appendix G. Independent Rationalizability |
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Appendix H. Injectivity and GenericityAppendix I. Extrinsic correlation Contd.; References; Chapter 5. Epistemic Conditions for Nash Equilibrium; 1 Introduction; 2 Interactive Belief Systems; 3 An Illustration; 4 Formal Statements and Proofs of the Results; 5 Tightness of the Results; 6 General (Infinite) Belief Systems; 7 Discussion; References; Chapter 6. Lexicographic Probabilities and Choice Under Uncertainty; 1 Introduction; 2 Subjective Expected Utility on Finite State Spaces; 3 Lexicographic Probability Systems and Non-Archimedean SEU Theory |
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4 Admissibility and Conditional Probabilities5 Lexicographic Conditional Probability Systems; 6 A "Numerical" Representation for Non-Archimedean SEU; 7 Stochastic Independence and Product Measures; Appendix; References; Chapter 7. Admissibility in Games; 1 Introduction; 2 Heuristic Treatment; 2.1. Lexicographic probabilities; 2.2. Rationality and common assumption of rationality; 2.3. Convex combinations; 2.4. Irrationality; 2.5. Characterization of RCAR; 2.6. Iterated admissibility; 2.7. A negative result; 2.8. The ingredients; 3 SAS's and the IA Set; 4 Lexicographic Probability Systems |
| Summary |
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 how players reason 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 a description of how the players reason about one another (including their reasoning about other players' reasoning). With this richer mathematical framework, it becomes possible to determi |
| Notes |
5 Assumption |
| Bibliography |
Includes bibliographical references and indexes |
| Notes |
Print version record |
| Subject |
Game theory.
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MATHEMATICS -- Applied.
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MATHEMATICS -- Probability & Statistics -- General.
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Game theory
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Spieltheorie
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| Form |
Electronic book
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| ISBN |
9789814513449 |
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981451344X |
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