An Introduction to Game Theory

• 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

"This is a textbook to be enjoyed both by professors and students, full of clever and often original applications and examples. Serious students who use this text are likely to emerge with a new way of thinking about much of what they see in the real world."--Ted Bergstrom, Professor of Economics, University of California, Santa Barbara "The book is just superb. I anticipate (based both on my own reading of the book, and comments from colleagues at other institutions) that this will be the standard text for introductory courses in game theory in political science departments for the foreseeable future."--Scott Gehlbach, Assistant Professor of Political Science, University of Wisconsin "What distinguishes this book from other texts is its remarkable combination of rigor and accessibility. The central concepts of game theory are presented with the mathematical precision suitable for a graduate course, but with an abundance of wide-ranging examples that will give undergraduate students a concrete understanding of what the concepts mean and how they may be used."--Charles A. Wilson, Professor of Economics, New York University "A great book, by far the best out there in the market in thoroughness and structure."--Dorothea Herreiner, Assistant Professor of Economics, Bowdoin College "The ideal textbook for applied game theory . . . . It teaches basic game theory from the ground up, using just enough clearly defined technical terminology and ranging from traditional basics to the most modern tools."--Randy Calvert, Professor of Political Science, Washington University in St. Louis "The approach is intuitive, yet rigorous. Key concepts are explained through a series of examples to guide students through analysis. The examples are then followed by interesting and challenging questions. The main strength is the impressive set of exercises . . . they are extremely well organized and incredibly broad, ranging from easy questions to those for adventurous students."--In-Koo Cho, William Kinkead Distinguished Professor of Economics, University of Illinois "The gentle pace of the material along with the plethora of examples drawn from economics (mainly) and political science seems to work very well with students."-Branislav L. Slantchev,Assistant Professor of Political Science, University of California, San Diego "The book is excellent. It is chock full of exercises that are both interesting and applicable to real issues, allowing me great flexibility in focusing on specific examples to illustrate the theory."--Christopher Proulx, Assistant Professor of Economics, University of California, Santa Barbara "This book provides a simple yet precise introduction into game theory, suitable for the undergraduate level. Author Martin J. Osborne makes use of a wide variety of examples from social and behavioral sciences to convey game-theoretic reasoning. Readers can expect to gain a thorough understanding without any previous knowledge of economics, political science, or any other social or behavioral science. No mathematics is assumed beyond that of basic high school."--Journal of Macroeconomics