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Game theory is the mathematical analysis of strategic interaction. In the fifty years since the appearance of von Neumann and Morgenstern's classic "Theory of Games and Economic Behavior" (Princeton, 1944), game theory has been widely applied to problems in economics. Until recently, however, its usefulness in political science has been underappreciated, in part because of the technical difficulty of the methods developed by economists. James Morrow's book is the first to provide a standard text adapting contemporary game theory to political analysis. It uses a minimum of mathematics to teach the essentials of game theory and contains problems and their solutions suitable for advanced undergraduate and graduate students in all branches of political science. Morrow begins with classical utility and game theory and ends with current research on repeated games and games of incomplete information. The book focuses on noncooperative game theory and its application to international relations, political economy, and American and comparative politics. Special attention is given to models of four topics: bargaining, legislative voting rules, voting in mass elections, and deterrence. An appendix reviews relevant mathematical techniques. Brief bibliographic essays at the end of each chapter suggest further readings, graded according to difficulty. This rigorous but accessible introduction to game theory will be of use not only to political scientists but also to psychologists, sociologists, and others in the social sciences.

List of Figures and Tables

Preface and Acknowledgments

Ch. 1Overview1

What Is Game Theory?1

What Can You Do with Game Theory?2

Four Problems in Political Science3Why Model?6

The Rational Choice Approach to Social Modeling7

Ch. 2Utility Theory16

The Concept of Rationality17

How Do Utility Functions Predict Actions?22

An Example: Nixon's Christmas Bombing25

Certainty, Risk, and Uncertainty28

Utility Theory under the Condition of Risk29

Some Common Misconceptions about Utility Theory33

Utility Functions and Types of Preferences34

A Simple Example: The Calculus of Deterrence38

Another Simple Example: The Decision to Vote43

Why Might Utility Theory Not Work?44

Ch. 3Specifying a Game51

Formalizing a Situation: Deterrence in the Cuban Missile Crisis51

Games in Extensive Form58

Games in Strategic Form65

Ch. 4Classical Game Theory73

Defining the Terms of Classical Game Theory74

Domination, Best Replies, and Equilibrium77

Mixed Strategies81

The Minmax Theorem and Equilibria of Two-Person, Zero-Sum Games89

Characteristics of Nash Equilibria91

Nash Equilibria and Common Conjectures94

Rationalizability98

Political Reform in Democracies101

Candidate Competition in the Spatial Model of Elections104

A Very Brief Introduction to Cooperative Game Theory111

Ch. 5Solving Extensive-Form Games: Backwards Induction and Subgame Perfection121

Backwards Induction124

Subgame Perfection128

Sophisticated Voting133

Agenda Control135

Legislative Rules and Structure-Induced Equilibria138

The Rubinstein Bargaining Model145

Bargaining in Legislatures149

Why Might Backwards Induction Yield Counterintuitive Results?156

Ch. 6Beliefs and Perfect Bayesian Equilibria161

Bayes's Theorem163

The Preference for Biased Information166

Perfect Bayesian Equilibria170

Nuclear Deterrence180

Ch. 7More on Noncooperative Equilibrium: Perfect and Sequential Equilibria188

Elimination of Weakly Dominated Strategies189

Perfect Equilibrium192

Sequential Equilibrium196

Deterrence and the Signaling of Resolve199

"Why Vote?" Redux212

Ch. 8Games of Limited Information and Restrictions on Beliefs219

Signaling Games222

The Informational Role of Congressional Committees227

Bargaining under Incomplete Information237

Deterrence and Out-of-Equilibrium Beliefs241

An Introduction to Restrictions on Beliefs244

"Cheap Talk" and Coordination250

Ch. 9Repeated Games260

Thinking about Repetition: Iterated Prisoner's Dilemma262

Folk Theorems268

Finite Repeated Games: The Chain Store Paradox279

Stationarity291

Retrospective Voting and Electoral Control293

Ch. 10Conclusion: Where Do We Go from Here?302

How Do Formal Models Increase Our Knowledge?302

The Weaknesses of Game Theory305How Does One Build a Model?311

Appendix 1: Basic Mathematical Knowledge315

Algebra315

Set Theory318

Relations and Functions320

Probability Theory320

Limits322

Differential Calculus323

Partial Derivatives and Lagrange Multipliers327

Integral Calculus329

The Idea of a Mathematical Proof331

Appendix 2: Answers to Selected Problems333

Notes345

Glossary of Terms in Game Theory349

Bibliography355

Index365

James D. Morrow is Senior Research Fellow at the Hoover Institution on War, Revolution and Peace at Stanford University.

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书籍介绍

Game theory is the mathematical analysis of strategic interaction. In the fifty years since the appearance of von Neumann and Morgenstern's classic "Theory of Games and Economic Behavior" (Princeton, 1944), game theory has been widely applied to problems in economics. Until recently, however, its usefulness in political science has been underappreciated, in part because of the technical difficulty of the methods developed by economists. James Morrow's book is the first to provide a standard text adapting contemporary game theory to political analysis. It uses a minimum of mathematics to teach the essentials of game theory and contains problems and their solutions suitable for advanced undergraduate and graduate students in all branches of political science. Morrow begins with classical utility and game theory and ends with current research on repeated games and games of incomplete information. The book focuses on noncooperative game theory and its application to international relations, political economy, and American and comparative politics. Special attention is given to models of four topics: bargaining, legislative voting rules, voting in mass elections, and deterrence. An appendix reviews relevant mathematical techniques. Brief bibliographic essays at the end of each chapter suggest further readings, graded according to difficulty. This rigorous but accessible introduction to game theory will be of use not only to political scientists but also to psychologists, sociologists, and others in the social sciences.