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Summary: 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, ext ...show moreensive games with imperfect information, and coalitional games. It includes over 100 exercises. ...show lessEdition/Copyright: 94
Osborne, Martin J. : University of Toronto
Rubinstein, Ariel : Tel Aviv University.
Chapter 1. Introduction
1.1 Game Theory
1.2 Games and Solutions
1.3 Game Theory and the Theory of Competitive Equilibrium
1.4 Rational Behavior
1.5 The Steady State and Deductive Interpretations
1.6 Bounded Rationality
1.7 Terminology and Notation
PART I. STRATEGIC GAMES
Chapter 2. Nash Equilibrium
2.1 Strategic Games
2.2 Nash Equilibrium
2.4 Existence of a Nash Equilibrium
2.5 Strictly Competitive Games
2.6 Bayesian Games : Strategic Games with Imperfect Information
Chapter 3. Mixed, Correlated, and Evolutionary Equilibrium
3.1 Mixed Strategy Nash Equilibrium
3.2 Interpretations of Mixed Strategy Nash Equilibrium
3.3 Correlated Equilibrium
3.4 Evolutionary Equilibrium
Chapter 4. Rationalizability and Iterated Elimination of Dominated Actions
4.2 Iterated Elimination of Strictly Dominated Actions
4.3 Iterated Elimination of Weakly Dominated Actions
Chapter 5. Knowledge and Equilibrium
5.1 A Model of Knowledge
5.2 Common Knowledge
5.3 Can People Agree to Disagree?
5.4 Knowledge and Solution Concepts
5.5 The Electronic Mail Game
PART II. EXTENSIVE GAMES WITH PERFECT INFORMATION
Chapter 6. Extensive Games with Perfect Information
6.1 Extensive Games with Perfect Information
6.2 Subgame Perfect Equilibrium
6.3 Two Extensions of the Definition of a Game
6.4 The Interpretation of a Strategy
6.5 Two Notable Finite Horizon Games
6.6 Iterated Elimination of Weakly Dominated Strategies
Chapter 7. Bargaining Games
7.1 Bargaining and Game Theory
7.2 A Bargaining Game of Alternating Offers
7.3 Subgame Perfect Equilibrium
7.4 Variations and Extensions
Chapter 8. Repeated Games
8.1 The Basic Idea
8.2 Infinitely Repeated Games vs.\ Finitely Repeated Games
8.3 Infinitely Repeated Games : Definitions
8.4 Strategies as Machines
8.5 Trigger Strategies : Nash Folk Theorems
8.6 Punishing for a Limited Length of Time : A Perfect Folk Theorem for the Limit of Means Criterion
8.7 Punishing the Punisher : A Perfect Folk Theorem for the Overtaking Criterion
8.8 Rewarding Players Who Punish : A Perfect Folk Theorem for the Discounting Criterion
8.9 The Structure of Subgame Perfect Equilibria Under the Discounting Criterion
8.10 Finitely Repeated Games
Chapter 9. Complexity Considerations in Repeated Games
9.1 Introduction 163
9.2 Complexity and the Machine Game
9.3 The Structure of the Equilibria of a Machine Game
9.4 The Case of Lexicographic Preferences
Chapter 10. Implementation Theory
10.2 The Implementation Problem
10.3 Implementation in Dominant Strategies
10.4 Nash Implementation
10.5 Subgame Perfect Equilibrium Implementation
PART III. EXTENSIVE GAMES WITH IMPERFECT INFORMATION
Chapter 11. Extensive Games with Imperfect Information
11.1 Extensive Games with Imperfect Information
11.2 Principles for the Equivalence of Extensive Games
11.3 Framing Effects and the Equivalence of Extensive Games
11.4 Mixed and Behavioral Strategies
11.5 Nash Equilibrium
Chapter 12. Sequential Equilibrium
12.1 Strategies and Beliefs
12.2 Sequential Equilibrium
12.3 Games with Observable Actions : Perfect Bayesian Equilibrium
12.4 Refinements of Sequential Equilibrium
12.5 Trembling Hand Perfect Equilibrium
PART IV. COALITIONAL GAMES
Chapter 13. The Core
13.1 Coalitional Games with Transferable Payoff
13.2 The Core
13.3 Nonemptiness of the Core
13.4 Markets with Transferable Payoff
13.5 Coalitional Games without Transferable Payoff
13.6 Exchange Economies
Chapter 14. Stable Sets, the Bargaining Set, and the Shapley Value
14.1 Two Approaches
14.2 The Stable Sets of von Neumann and Morgenstern
14.3 The Bargaining Set, Kernel, and Nucleolus
14.4 The Shapley Value
Chapter 15. The Nash Solution
15.1 Bargaining Problems
15.2 The Nash Solution : Definition and Characterization
15.3 An Axiomatic Definition
15.4 The Nash Solution and the Bargaining Game of Alternating Offers
15.5 An Exact Implementation of the Nash Solution
List of Results
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