A Course in Game Theory,9780262650403

A Course in Game Theory

by ;
ISBN13: 9780262650403
ISBN10: 0262650401
Format: Paperback
Pub. Date: 1994-07-12
Publisher(s): The MIT Press
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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, extensive games with imperfect information, and coalitional games. It includes over 100 exercises.

Author Biography

Martin J. Osborne is Professor of Economics at the University of Toronto.

Ariel Rubinstein is Professor of Economics at Tel Aviv University and New York University.

Table of Contents

Preface xi
Introduction
1(8)
Game Theory
1(1)
Games and Solutions
2(1)
Game Theory and the Theory of Competitive Equilibrium
3(1)
Rational Behavior
4(1)
The Steady State and Deductive Interpretations
5(1)
Bounded Rationality
6(1)
Terminology and Notation
6(3)
Notes
8(1)
I Strategic Games 9(78)
Nash Equilibrium
11(20)
Strategic Games
11(3)
Nash Equilibrium
14(1)
Examples
15(4)
Existence of a Nash Equilibrium
19(2)
Strictly Competitive Games
21(3)
Bayesian Games: Strategic Games with Imperfect Information
24(7)
Notes
29(2)
Mixed, Correlated, and Evolutionary Equilibrium
31(22)
Mixed Strategy Nash Equilibrium
31(6)
Interpretations of Mixed Strategy Nash Equilibrium
37(7)
Correlated Equilibrium
44(4)
Evolutionary Equilibrium
48(5)
Notes
51(2)
Rationalizability and Iterated Elimination of Dominated Actions
53(14)
Rationalizability
53(5)
Iterated Elimination of Strictly Dominated Actions
58(4)
Iterated Elimination of Weakly Dominated Actions
62(5)
Notes
64(3)
Knowledge and Equilibrium
67(20)
A Model of Knowledge
67(6)
Common Knowledge
73(2)
Can People Agree to Disagree?
75(1)
Knowledge and Solution Concepts
76(5)
The Electronic Mail Game
81(6)
Notes
84(3)
II Extensive Games with Perfect Information 87(110)
Extensive Games with Perfect Information
89(28)
Extensive Games with Perfect Information
89(8)
Subgame Perfect Equilibrium
97(4)
Two Extensions of the Definition of a Game
101(2)
The Interpreation of a Strategy
103(2)
Two Notable Finite Horizon Games
105(3)
Iterated Elimination of Weakly Dominated Strategies
108(9)
Notes
114(3)
Bargaining Games
117(16)
Bargaining and Game Theory
117(1)
A Bargaining Game of Alternating Offers
118(3)
Subgame Perfect Equilibrium
121(6)
Variations and Extensions
127(6)
Notes
131(2)
Repeated Games
133(30)
The Basic Idea
133(1)
Infinitely Repeated Games vs. Finitely Repeated Games
134(2)
Infinitely Repeated Games: Definitions
136(4)
Strategies as Machines
140(3)
Trigger Strategies: Nash Folk Theorems
143(3)
Punishing for a Limited Length of Time: A Perfect Folk Theorem for the Limit of Means Criterion
146(3)
Punishing the Punisher: A Perfect Folk Theorem for the Overtaking Criterion
149(1)
Rewarding Players Who Punish: A Perfect Folk Theorem for the Discounting Criterion
150(3)
The Structure of Subgame Perfect Equilibria Under the Discounting Criterion
153(2)
Finitely Repeated Games
155(8)
Notes
160(3)
Complexity Considerations in Repeated Games
163(14)
Introduction
163(1)
Complexity and the Machine Game
164(4)
The Structure of the Equilibria of a Machine Game
168(4)
The Case of Lexicographic Preferences
172(5)
Notes
175(2)
Implementation Theory
177(20)
Introduction
177(1)
The Implementation Problem
178(2)
Implementation in Dominant Strategies
180(5)
Nash Implementation
185(6)
Subgame Perfect Equilibrium Implementation
191(6)
Notes
195(2)
III Extensive Games with Imperfect Information 197(58)
Extensive Games with Imperfect Information
199(20)
Extensive Games with Imperfect Information
199(5)
Principles for the Equivalence of Extensive Games
204(5)
Framing Effects and the Equivalence of Extensive Games
209(3)
Mixed and Behavioral Strategies
212(4)
Nash Equilibrium
216(3)
Notes
217(2)
Sequential Equilibrium
219(36)
Strategies and Beliefs
219(3)
Sequential Equilibrium
222(9)
Games with Observable Actions: Perfect Bayesian Equilibrium
231(12)
Refinements of Sequential Equilibrium
243(3)
Trembling Hand Perfect Equilibrium
246(9)
Notes
254(1)
IV Coalitional Games 255(58)
The Core
257(20)
Coalitional Games with Transferable Payoff
257(1)
The Core
258(4)
Nonemptiness of the Core
262(1)
Markets with Transferable Payoff
263(5)
Coalitional Games without Transferable Payoff
268(1)
Exchange Economies
269(8)
Notes
274(3)
Stable Sets, the Bargaining Set, and the Shapley Value
277(22)
Two Approaches
277(1)
The Stable Sets of von Neumann and Morgenstern
278(3)
The Bargaining Set, Kernel, and Nucleolus
281(8)
The Shapley Value
289(10)
Notes
297(2)
The Nash Solution
299(14)
Bargaining Problems
299(2)
The Nash Solution: Definition and Characterization
301(4)
An Axiomatic Definition
305(5)
The Nash Solution and the Bargaining Game of Alternating Offers
310(1)
An Exact Implementation of the Nash Solution
311(2)
Notes
312(1)
List of Results 313(8)
References 321(20)
Index 341

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