Game Theory for Political Scientists / Edition 1

by James D. Morrow

Overview

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.

Product Details

ISBN-13:	9780691034300
Publisher:	Princeton University Press
Publication date:	12/19/1994
Edition description:	New Edition
Pages:	400
Product dimensions:	6.00(w) x 9.25(h) x (d)

About the Author

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

Table of Contents

List of Figures and Tables

Preface and Acknowledgments

Ch. 1 Overview 1

What Is Game Theory? 1

What Can You Do with Game Theory? 2

Four Problems in Political Science 3

Why Model? 6

The Rational Choice Approach to Social Modeling 7

Ch. 2 Utility Theory 16

The Concept of Rationality 17

How Do Utility Functions Predict Actions? 22

An Example: Nixon's Christmas Bombing 25

Certainty, Risk, and Uncertainty 28

Utility Theory under the Condition of Risk 29

Some Common Misconceptions about Utility Theory 33

Utility Functions and Types of Preferences 34

A Simple Example: The Calculus of Deterrence 38

Another Simple Example: The Decision to Vote 43

Why Might Utility Theory Not Work? 44

Ch. 3 Specifying a Game 51

Formalizing a Situation: Deterrence in the Cuban Missile Crisis 51

Games in Extensive Form 58

Games in Strategic Form 65

Ch. 4 Classical Game Theory 73

Defining the Terms of Classical Game Theory 74

Domination, Best Replies, and Equilibrium 77

Mixed Strategies 81

The Minmax Theorem and Equilibria of Two-Person, Zero-Sum Games 89

Characteristics of Nash Equilibria 91

Nash Equilibria and Common Conjectures 94

Rationalizability 98

Political Reform in Democracies 101

Candidate Competition in the Spatial Model of Elections 104

A Very Brief Introduction to Cooperative Game Theory 111

Ch. 5 Solving Extensive-Form Games: Backwards Induction and Subgame Perfection 121

Backwards Induction 124

Subgame Perfection 128

Sophisticated Voting 133

Agenda Control 135

Legislative Rules and Structure-Induced Equilibria 138

The Rubinstein Bargaining Model 145

Bargaining in Legislatures 149

Why Might Backwards Induction Yield Counterintuitive Results? 156

Ch. 6 Beliefs and Perfect Bayesian Equilibria 161

Bayes's Theorem 163

The Preference for Biased Information 166

Perfect Bayesian Equilibria 170

Nuclear Deterrence 180

Ch. 7 More on Noncooperative Equilibrium: Perfect and Sequential Equilibria 188

Elimination of Weakly Dominated Strategies 189

Perfect Equilibrium 192

Sequential Equilibrium 196

Deterrence and the Signaling of Resolve 199

"Why Vote?" Redux 212

Ch. 8 Games of Limited Information and Restrictions on Beliefs 219

Signaling Games 222

The Informational Role of Congressional Committees 227

Bargaining under Incomplete Information 237

Deterrence and Out-of-Equilibrium Beliefs 241

An Introduction to Restrictions on Beliefs 244

"Cheap Talk" and Coordination 250

Ch. 9 Repeated Games 260

Thinking about Repetition: Iterated Prisoner's Dilemma 262

Folk Theorems 268

Finite Repeated Games: The Chain Store Paradox 279

Stationarity 291

Retrospective Voting and Electoral Control 293

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

How Do Formal Models Increase Our Knowledge? 302

The Weaknesses of Game Theory 305

How Does One Build a Model? 311

Appendix 1: Basic Mathematical Knowledge 315

Algebra 315

Set Theory 318

Relations and Functions 320

Probability Theory 320

Limits 322

Differential Calculus 323

Partial Derivatives and Lagrange Multipliers 327

Integral Calculus 329

The Idea of a Mathematical Proof 331

Appendix 2: Answers to Selected Problems 333

Notes 345

Glossary of Terms in Game Theory 349

Bibliography 355

Index 365

Editorial Reviews

"James Morrow's superb book provides the best account of ideas from game theory tailored to the interests of political scientists, which is currently available."

The Times Higher Education Supplement

"James Morrow's superb book provides the best account of ideas from game theory tailored to the interests of political scientists, which is currently available."—The Times Higher Education Supplement

From the Publisher