A Course in Game Theory

ISBN: 9780262359757 | Copyright 1994

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A Course in Game Theory presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its basic concepts. The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises.

Martin Osborne and Ariel Rubinstein have made most of their theoretical contributions on the strategic side, and yet they devote a nice portion of the book to cooperative game theory. I recommend this book highly. It is beautifully done, and it recognized the importance of the cooperative theory.

Robert J. Aumann Professor of Mathematics, The Hebrew
University of Jerusalem
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Preface (pg. xi)
1 Introduction (pg. 1)
1.1 Game Theory (pg. 1)
1.2 Games and Solutions (pg. 2)
1.3 Game Theory and the Theory of Competitive Equilibrium (pg. 3)
1.4 Rational Behavior (pg. 4)
1.5 The Steady State and Deductive Interpretations (pg. 5)
1.6 Bounded Rationality (pg. 6)
1.7 Terminology and Notation (pg. 6)
Notes (pg. 8)
I Strategic Games (pg. 9)
2 Nash Equilibrium (pg. 11)
2.1 Strategic Games (pg. 11)
2.2 Nash Equilibrium (pg. 14)
2.3 Examples (pg. 15)
2.4 Existence of a Nash Equilibrium (pg. 19)
2.5 Strictly Competitive Games (pg. 21)
2.6 Bayesian Games: Strategic Games with Imperfect Information (pg. 24)
Notes (pg. 29)
3 Mixed, Correlated, and Evolutionary Equilibrium (pg. 31)
3.1 Mixed Strategy Nash Equilibrium (pg. 31)
3.2 Interpretations of Mixed Strategy Nash Equilibrium (pg. 37)
3.3 Correlated Equilibrium (pg. 44)
3.4 Evolutionary Equilibrium (pg. 48)
Notes (pg. 51)
4 Rationalizability and Iterated Elimination of Dominated Actions (pg. 53)
4.1 Rationalizability (pg. 53)
4.2 Iterated Elimination of Strictly Dominated Actions (pg. 58)
4.3 Iterated Elimination of Weakly Dominated Actions (pg. 62)
Notes (pg. 64)
5 Knowledge and Equilibrium (pg. 67)
5.1 A Model of Knowledge (pg. 67)
5.2 Common Knowledge (pg. 73)
5.3 Can People Agree to Disagree? (pg. 75)
5.4 Knowledge and Solution Concepts (pg. 76)
5.5 The Electronic Mail Game (pg. 81)
Notes (pg. 84)
II Extensive Games with Perfect Information (pg. 87)
6 Extensive Games with Perfect Information (pg. 89)
6.1 Extensive Games with Perfect Information (pg. 89)
6.2 Subgame Perfect Equilibrium (pg. 97)
6.3 Two Extensions of the Definition of a Game (pg. 101)
6.4 The Interpretation of a Strategy (pg. 103)
6.5 Two Notable Finite Horizon Games (pg. 105)
6.6 Iterated Elimination of Weakly Dominated Strategies (pg. 108)
Notes (pg. 114)
7 Bargaining Games (pg. 117)
7.1 Bargaining and Game Theory (pg. 117)
7.2 A Bargaining Game of Alternating Offers (pg. 118)
7.3 Subgame Perfect Equilibrium (pg. 121)
7.4 Variations and Extensions (pg. 127)
Notes (pg. 131)
8 Repeated Games (pg. 133)
8.1 The Basic Idea (pg. 133)
8.2 Infinitely Repeated Games vs. Finitely Repeated Games (pg. 134)
8.3 Infinitely Repeated Games: Definitions (pg. 136)
8.4 Strategies as Machines (pg. 140)
8.5 Trigger Strategies: Nash Folk Theorems (pg. 143)
8.6 Punishing for a Limited Length of Time: A Perfect Folk Theorem for the Limit of Means Criterion (pg. 146)
8.7 Punishing the Punisher: A Perfect Folk Theorem for the Overtaking Criterion (pg. 149)
8.8 Rewarding Players Who Punish: A Perfect Folk Theorem for the Discounting Criterion (pg. 150)
8.9 The Structure of Subgame Perfect Equilibria Under the Discounting Criterion (pg. 153)
8.10 Finitely Repeated Games (pg. 155)
Notes (pg. 160)
9 Complexity Considerations in Repeated Games (pg. 163)
9.1 Introduction (pg. 163)
9.2 Complexity and the Machine Game (pg. 164)
9.3 The Structure of the Equilibria of a Machine Game (pg. 168)
9.4 The Case of Lexicographic Preferences (pg. 172)
Notes (pg. 175)
10 Implementation Theory (pg. 177)
10.1 Introduction (pg. 177)
10.2 The Implementation Problem (pg. 178)
10.3 Implementation in Dominant Strategies (pg. 180)
10.4 Nash Implementation (pg. 185)
10.5 Subgame Perfect Equilibrium Implementation (pg. 191)
Notes (pg. 195)
III Extensive Games with Imperfect Information (pg. 197)
11 Extensive Games with Imperfect Information (pg. 199)
11.1 Extensive Games with Imperfect Information (pg. 199)
11.2 Principles for the Equivalence of Extensive Games (pg. 204)
11.3 Framing Effects and the Equivalence of Extensive Games (pg. 209)
11.4 Mixed and Behavioral Strategies (pg. 212)
11.5 Nash Equilibrium (pg. 216)
Notes (pg. 217)
12 Sequential Equilibrium (pg. 219)
12.1 Strategies and Beliefs (pg. 219)
12.2 Sequential Equilibrium (pg. 222)
12.3 Games with Observable Actions: Perfect Bayesian Equilibrium (pg. 231)
12.4 Refinements of Sequential Equilibrium (pg. 243)
12.5 Trembling Hand Perfect Equilibrium (pg. 246)
Notes (pg. 254)
IV Coalitional Games (pg. 255)
13 The Core (pg. 257)
13.1 Coalitional Games with Transferable Payoff (pg. 257)
13.2 The Core (pg. 258)
13.3 Nonemptiness of the Core (pg. 262)
13.4 Markets with Transferable Payoff (pg. 263)
13.5 Coalitional Games without Transferable Payoff (pg. 268)
13.6 Exchange Economies (pg. 269)
Notes (pg. 274)
14 Stable Sets, the Bargaining Set, and the Shapley Value (pg. 277)
14.1 Two Approaches (pg. 277)
14.2 The Stable Sets of von Neumann and Morgenstern (pg. 278)
14.3 The Bargaining Set, Kernel, and Nucleolus (pg. 281)
14.4 The Shapley Value (pg. 289)
Notes (pg. 297)
15 The Nash Solution (pg. 299)
15.1 Bargaining Problems (pg. 299)
15.2 The Nash Solution: Definition and Characterization (pg. 301)
15.3 An Axiomatic Definition (pg. 305)
15.4 The Nash Solution and the Bargaining Game of Alternating Offers (pg. 310)
15.5 An Exact Implementation of the Nash Solution (pg. 311)
Notes (pg. 312)
List of Results (pg. 313)
References (pg. 321)
Index (pg. 341)
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