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Introduction to Game Theory

Introduction to Game Theory - 04 edition

ISBN13: 978-0195128956

Cover of Introduction to Game Theory 04 (ISBN 978-0195128956)
ISBN13: 978-0195128956
ISBN10: 0195128958
Cover type: Hardback
Edition/Copyright: 04
Publisher: Oxford University Press
Published: 2004
International: No

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Introduction to Game Theory - 04 edition

ISBN13: 978-0195128956

Martin J. Osborne

ISBN13: 978-0195128956
ISBN10: 0195128958
Cover type: Hardback
Edition/Copyright: 04
Publisher: Oxford University Press

Published: 2004
International: No
Summary

Game-theoretic reasoning pervades economic theory and is used widely in other social and behavioral sciences. An Introduction to Game Theory, by Martin J. Osborne, presents the main principles of game theory and shows how they can be used to understand economic, social, political, and biological phenomena. The book introduces in an accessible manner the main ideas behind the theory rather than their mathematical expression. All concepts are defined precisely, and logical reasoning is used throughout. The book requires an understanding of basic mathematics but assumes no specific knowledge of economics, political science, or other social or behavioral sciences.

Coverage includes the fundamental concepts of strategic games, extensive games with perfect information, and coalitional games; the more advanced subjects of Bayesian games and extensive games with imperfect information; and the topics of repeated games, bargaining theory, evolutionary equilibrium, rationalizability, and maxminimization. The book offers a wide variety of illustrations from the social and behavioral sciences and more than 280 exercises. Each topic features examples that highlight theoretical points and illustrations that demonstrate how the theory may be used. Explaining the key concepts of game theory as simply as possible while maintaining complete precision, An Introduction to Game Theory is ideal for undergraduate and introductory graduate courses in game theory.

Author Bio

Osborne, Martin J. : University of Toronto, Canada

Table of Contents

Each chapter ends with notes.

Preface

1. Introduction

1.1. What is Game Theory?
1.1.1. An Outline of the History of Game Theory
1.1.2. John von Neumann
1.2. The Theory of Rational Choice
1.3. Coming Attractions: Interacting Decision-Makers

I. GAMES WITH PERFECT INFORMATION

2. Nash Equilibrium: Theory

2.1. Strategic Games
2.2. Example: The Prisoner's Dilemma
2.3. Example: Bach or Stravinsky?
2.4. Example: Matching Pennies
2.5. Example: The Stag Hunt
2.6. Nash Equilibrium
2.6.1. John F. Nash, Jr.
2.6.2. Studying Nash Equilibrium Experimentally
2.7. Examples of Nash Equilibrium
2.7.1. Experimental Evidence on the Prisoner's Dilemma
2.7.2. Focal Points
2.8. Best Response Functions
2.9. Dominated Actions
2.10. Equilibrium in a Single Population: Symmetric Games and Symmetric Equilibria

3. Nash Equilibrium: Illustrations

3.1. Cournot's Model of Oligopoly
3.2. Bertrand's Model of Oligopoly
3.2.1. Cournot, Bertrand, and Nash: Some Historical Notes
3.3. Electoral Competition
3.4. The War of Attrition
3.5. Auctions
3.5.1. Auctions from Babylonia to eBay
3.6. Accident Law

4. Mixed Strategy Equilibrium

4.1. Introduction
4.1.1. Some Evidence on Expected Payoff Functions
4.2. Strategic Games in Which Players May Randomize
4.3. Mixed Strategy Nash Equilibrium
4.4. Dominated Actions
4.5. Pure Equilibria When Randomization is Allowed
4.6. Illustration: Expert Diagnosis
4.7. Equilibrium in a Single Population
4.8. Illustration: Reporting a Crime
4.8.1. Reporting a Crime: Social Psychology and Game Theory
4.9. The Formation of Players' Beliefs
4.10. Extension: Finding All Mixed Strategy Nash Equilibria
4.11. Extension: Games in Which Each Player Has a Continuum of Actions
4.12. Appendix: Representing Preferences by Expected Payoffs

5. Extensive Games with Perfect Information: Theory

5.1. Extensive Games with Perfect Information
5.2. Strategies and Outcomes
5.3. Nash Equilibrium
5.4. Subgame Perfect Equilibrium
5.5. Finding Subgame Perfect Equilibria of Finite Horizon Games: Backward Induction
5.5.1. Ticktacktoe, Chess, and Related Games

6. Extensive Games With Perfect Information: Illustrations

6.1. The Ultimatum Game, the Holdup Game, and Agenda Control
6.1.1. Experiments on the Ultimatum Game
6.2. Stackelberg's Model of Duopoly
6.3. Buying Votes
6.4. A Race

7. Extensive Games With Perfect Information: Extensions and Discussion

7.1. Allowing for Simultaneous Moves
7.1.1. More Experimental Evidence on Subgame Perfect Equilibrium
7.2. Illustration: Entry into a Monopolized Industry
7.3. Illustration: Electoral Competition with Strategic Voters
7.4. Illustration: Committee Decision-Making
7.5. Illustration: Exit from a Declining Industry
7.6. Allowing for Exogenous Uncertainty
7.7. Discussion: Subgame Perfect Equilibrium and Backward Induction
7.7.1. Experimental Evidence on the Centipede Game

8. Coalitional Games and the Core

8.1. Coalitional Games
8.2. The Core
8.3. Illustration: Ownership and the Distribution of Wealth
8.4. Illustration: Exchanging Homogeneous Horses
8.5. Illustration: Exchanging Heterogeneous Houses
8.6. Illustration: Voting
8.7. Illustration: Matching
8.7.1. Matching Doctors with Hospitals
8.8. Discussion: Other Solution Concepts

II. GAMES WITH IMPERFECT INFORMATION

9.1. Motivational Examples
9.2. General Definitions
9.3. Two Examples Concerning Information
9.4. Illustration: Cournot's Duopoly Game with Imperfect Information
9.5. Illustration: Providing a Public Good
9.6. Illustration: Auctions
9.6.1. Auctions of the Radio Spectrum
9.7. Illustration: Juries
9.8. Appendix: Auctions with an Arbitrary Distribution of Valuations

10. Extensive Games with Imperfect Information

10.1. Extensive Games with Imperfect Information
10.2. Strategies
10.3. Nash Equilibrium
10.4. Beliefs and Sequential Equilibrium
10.5. Signaling Games.
10.6. Illustration: Conspicuous Expenditure as a Signal of Quality
10.7. Illustration: Education as a Signal Of Ability
10.8. Illustration: Strategic Information Transmission
10.9. Illustration: Agenda Control with Imperfect Information

III. VARIANTS AND EXTENSIONS

11. Strictly Competitive Games and Maxminimization

11.1. Maxminimization
11.2. Maxminimization and Nash Equilibrium
11.3. Strictly Competitive Games
11.4. Maxminimization and Nash Equilibrium in Strictly Competitive Games
11.4.1. Maxminimization: Some History
11.4.2. Empirical Tests: Experiments, Tennis, and Soccer

12. Rationalizability

12.1. Rationalizability
12.2. Iterated Elimination of Strictly Dominated Actions
12.3. Iterated Elimination of Weakly Dominated Actions
12.4. Dominance Solvability

13. Evolutionary Equilibrium

13.1. Monomorphic Pure Strategy Equilibrium
13.1.1. Evolutionary Game Theory: Some History
13.2. Mixed Strategies and Polymorphic Equilibrium
13.3. Asymmetric Contests
13.3.1. Side-blotched lizards
13.3.2. Explaining the Outcomes of Contests in Nature
13.4. Variation on a Theme: Sibling Behavior
13.5. Variation on a Theme: The Nesting Behavior of Wasps
13.6. Variation on a Theme: The Evolution of the Sex Ratio

14. Repeated Games: The Prisoner's Dilemma

14.1. The Main Idea
14.2. Preferences
14.3. Repeated Games
14.4. Finitely Repeated Prisoner's Dilemma
14.5. Infinitely Repeated Prisoner's Dilemma
14.6. Strategies in an Infinitely Repeated Prisoner's Dilemma
14.7. Some Nash Equilibria of an Infinitely Repeated Prisoner's Dilemma
14.8. Nash Equilibrium Payoffs of an Infinitely Repeated Prisoner's Dilemma
14.8.1. Experimental Evidence
14.9. Subgame Perfect Equilibria and the One-Deviation Property
14.9.1. Axelrod's Tournaments
14.10. Some Subgame Perfect Equilibria of an Infinitely Repeated Prisoner's Dilemma
14.10.1. Reciprocal Altruism Among Sticklebacks
14.11. Subgame Perfect Equilibrium Payoffs of an Infinitely Repeated Prisoner's Dilemma
14.11.1. Medieval Trade Fairs
14.12. Concluding Remarks

15. Repeated Games: General Results

15.1. Nash Equilibria of General Infinitely Repeated Games
15.2. Subgame Perfect Equilibria of General Infinitely Repeated Games
15.3. Finitely Repeated Games
15.4. Variation on a Theme: Imperfect Observability

16. Bargaining

16.1. Bargaining as an Extensive Game
16.2. Illustration: Trade in a Market
16.3. Nash's Axiomatic Model
16.4. Relation Between Strategic and Axiomatic Models

17. Appendix: Mathematics

17.1. Numbers
17.2. Sets
17.3. Functions
17.4. Profiles
17.5. Sequences
17.6. Probability
17.7. Proofs