The language of game theory: putting epistemics into the mathematics of games
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Publishing Company
c2014
|
| Schriftenreihe: | World Scientific series in economic theory
v.5 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 |
| Beschreibung: | 5 Assumption 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 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 Includes bibliographical references and indexes |
| Beschreibung: | xxxiv, 263 pages |
| ISBN: | 9789814513449 981451344X 9814513431 9789814513432 |
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| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a Includes bibliographical references and indexes | ||
| 650 | 4 | |a Epistemics | |
| 650 | 4 | |a Game theory | |
| 650 | 4 | |a Mathematics | |
| 650 | 7 | |a MATHEMATICS / Applied |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Probability & Statistics / General |2 bisacsh | |
| 650 | 7 | |a Game theory |2 fast | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Game theory | |
| 650 | 0 | 7 | |a Spieltheorie |0 (DE-588)4056243-8 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Brandenburger, Adam |
| author_facet | Brandenburger, Adam |
| author_role | aut |
| author_sort | Brandenburger, Adam |
| author_variant | a b ab |
| building | Verbundindex |
| bvnumber | BV043777755 |
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| dewey-full | 519.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.3 |
| dewey-search | 519.3 |
| dewey-sort | 3519.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043777755 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:34:50Z |
| institution | BVB |
| isbn | 9789814513449 981451344X 9814513431 9789814513432 |
| language | English |
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| physical | xxxiv, 263 pages |
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| spelling | Brandenburger, Adam Verfasser aut The language of game theory putting epistemics into the mathematics of games Adam Brandenburger Singapore World Scientific Publishing Company c2014 xxxiv, 263 pages txt rdacontent c rdamedia cr rdacarrier World Scientific series in economic theory v.5 5 Assumption 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 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 Includes bibliographical references and indexes Epistemics Game theory Mathematics MATHEMATICS / Applied bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Game theory fast Mathematik Spieltheorie (DE-588)4056243-8 gnd rswk-swf Spieltheorie (DE-588)4056243-8 s 1\p DE-604 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Brandenburger, Adam The language of game theory putting epistemics into the mathematics of games Epistemics Game theory Mathematics MATHEMATICS / Applied bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Game theory fast Mathematik Spieltheorie (DE-588)4056243-8 gnd |
| subject_GND | (DE-588)4056243-8 |
| title | The language of game theory putting epistemics into the mathematics of games |
| title_auth | The language of game theory putting epistemics into the mathematics of games |
| title_exact_search | The language of game theory putting epistemics into the mathematics of games |
| title_full | The language of game theory putting epistemics into the mathematics of games Adam Brandenburger |
| title_fullStr | The language of game theory putting epistemics into the mathematics of games Adam Brandenburger |
| title_full_unstemmed | The language of game theory putting epistemics into the mathematics of games Adam Brandenburger |
| title_short | The language of game theory |
| title_sort | the language of game theory putting epistemics into the mathematics of games |
| title_sub | putting epistemics into the mathematics of games |
| topic | Epistemics Game theory Mathematics MATHEMATICS / Applied bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Game theory fast Mathematik Spieltheorie (DE-588)4056243-8 gnd |
| topic_facet | Epistemics Game theory Mathematics MATHEMATICS / Applied MATHEMATICS / Probability & Statistics / General Mathematik Spieltheorie |
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