Game Theory for Political Scientists

Game theory is the mathematical analysis of strategic interaction. In the fifty years since the appearance of von Neumann and Morgenstern's classicTheory 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.

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

List of Figures and Tables
Preface and Acknowledgments
Overview	p. 1
What Is Game Theory?	p. 1
What Can You Do with Game Theory?	p. 2
Four Problems in Political Science	p. 3
Why Model?	p. 6
The Rational Choice Approach to Social Modeling	p. 7
Utility Theory	p. 16
The Concept of Rationality	p. 17
How Do Utility Functions Predict Actions?	p. 22
An Example: Nixon's Christmas Bombing	p. 25
Certainty, Risk, and Uncertainty	p. 28
Utility Theory under the Condition of Risk	p. 29
Some Common Misconceptions about Utility Theory	p. 33
Utility Functions and Types of Preferences	p. 34
A Simple Example: The Calculus of Deterrence	p. 38
Another Simple Example: The Decision to Vote	p. 43
Why Might Utility Theory Not Work?	p. 44
Specifying a Game	p. 51
Formalizing a Situation: Deterrence in the Cuban Missile Crisis	p. 51
Games in Extensive Form	p. 58
Games in Strategic Form	p. 65
Classical Game Theory	p. 73
Defining the Terms of Classical Game Theory	p. 74
Domination, Best Replies, and Equilibrium	p. 77
Mixed Strategies	p. 81
The Minmax Theorem and Equilibria of Two-Person, Zero-Sum Games	p. 89
Characteristics of Nash Equilibria	p. 91
Nash Equilibria and Common Conjectures	p. 94
Rationalizability	p. 98
Political Reform in Democracies	p. 101
Candidate Competition in the Spatial Model of Elections	p. 104
A Very Brief Introduction to Cooperative Game Theory	p. 111
Solving Extensive-Form Games: Backwards Induction and Subgame Perfection	p. 121
Backwards Induction	p. 124
Subgame Perfection	p. 128
Sophisticated Voting	p. 133
Agenda Control	p. 135
Legislative Rules and Structure-Induced Equilibria	p. 138
The Rubinstein Bargaining Model	p. 145
Bargaining in Legislatures	p. 149
Why Might Backwards Induction Yield Counterintuitive Results?	p. 156
Beliefs and Perfect Bayesian Equilibria	p. 161
Bayes's Theorem	p. 163
The Preference for Biased Information	p. 166
Perfect Bayesian Equilibria	p. 170
Nuclear Deterrence	p. 180
More on Noncooperative Equilibrium: Perfect and Sequential Equilibria	p. 188
Elimination of Weakly Dominated Strategies	p. 189
Perfect Equilibrium	p. 192
Sequential Equilibrium	p. 196
Deterrence and the Signaling of Resolve	p. 199
"Why Vote?" Redux	p. 212
Games of Limited Information and Restrictions on Beliefs	p. 219
Signaling Games	p. 222
The Informational Role of Congressional Committees	p. 227
Bargaining under Incomplete Information	p. 237
Deterrence and Out-of-Equilibrium Beliefs	p. 241
An Introduction to Restrictions on Beliefs	p. 244
"Cheap Talk" and Coordination	p. 250
Repeated Games	p. 260
Thinking about Repetition: Iterated Prisoner's Dilemma	p. 262
Folk Theorems	p. 268
Finite Repeated Games: The Chain Store Paradox	p. 279
Stationarity	p. 291
Retrospective Voting and Electoral Control	p. 293
Conclusion: Where Do We Go from Here?	p. 302
How Do Formal Models Increase Our Knowledge?	p. 302
The Weaknesses of Game Theory	p. 305
How Does One Build a Model?	p. 311
Appendix 1: Basic Mathematical Knowledge	p. 315
Algebra	p. 315
Set Theory	p. 318
Relations and Functions	p. 320
Probability Theory	p. 320
Limits	p. 322
Differential Calculus	p. 323
Partial Derivatives and Lagrange Multipliers	p. 327
Integral Calculus	p. 329
The Idea of a Mathematical Proof	p. 331
Answers to Selected Problems	p. 333
Notes	p. 345
Glossary of Terms in Game Theory	p. 349
Bibliography	p. 355
Index	p. 365
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Game Theory for Political Scientists

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