An Introduction to Game Theory

Description

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.

 

Table of Contents

Preface

Each chapter ends with notes.

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