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 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 ...

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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
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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
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