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The language of game theory : putting epistemics into the mathematics of games /
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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, NJ :
World Scientific Publishing Company,
©2014.
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| Colección: | World Scientific series in economic theory ;
v. 5. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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.
- 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.
- 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.
- 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.