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 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.

Table of Contents:
List of Figures and TablesPreface and AcknowledgmentsCh. 1Overview1What Is Game Theory?1What Can You Do with Game Theory?2Four Problems in Political Science3Why Model?6The Rational Choice Approach to Social Modeling7Ch. 2Utility Theory16The Concept of Rationality17How Do Utility Functions Predict Actions?22An Example: Nixon's Christmas Bombing25Certainty, Risk, and Uncertainty28Utility Theory under the Condition of Risk29Some Common Misconceptions about Utility Theory33Utility Functions and Types of Preferences34A Simple Example: The Calculus of Deterrence38Another Simple Example: The Decision to Vote43Why Might Utility Theory Not Work?44Ch. 3Specifying a Game51Formalizing a Situation: Deterrence in the Cuban Missile Crisis51Games in Extensive Form58Games in Strategic Form65Ch. 4Classical Game Theory73Defining the Terms of Classical Game Theory74Domination, Best Replies, and Equilibrium77Mixed Strategies81The Minmax Theorem and Equilibria of Two-Person, Zero-Sum Games89Characteristics of Nash Equilibria91Nash Equilibria and Common Conjectures94Rationalizability98Political Reform in Democracies101Candidate Competition in the Spatial Model of Elections104A Very Brief Introduction to Cooperative Game Theory111Ch. 5Solving Extensive-Form Games: Backwards Induction and Subgame Perfection121Backwards Induction124Subgame Perfection128Sophisticated Voting133Agenda Control135Legislative Rules and Structure-Induced Equilibria138The Rubinstein Bargaining Model145Bargaining in Legislatures149Why Might Backwards Induction Yield Counterintuitive Results?156Ch. 6Beliefs and Perfect Bayesian Equilibria161Bayes's Theorem163The Preference for Biased Information166Perfect Bayesian Equilibria170Nuclear Deterrence180Ch. 7More on Noncooperative Equilibrium: Perfect and Sequential Equilibria188Elimination of Weakly Dominated Strategies189Perfect Equilibrium192Sequential Equilibrium196Deterrence and the Signaling of Resolve199"Why Vote?" Redux212Ch. 8Games of Limited Information and Restrictions on Beliefs219Signaling Games222The Informational Role of Congressional Committees227Bargaining under Incomplete Information237Deterrence and Out-of-Equilibrium Beliefs241An Introduction to Restrictions on Beliefs244"Cheap Talk" and Coordination250Ch. 9Repeated Games260Thinking about Repetition: Iterated Prisoner's Dilemma262Folk Theorems268Finite Repeated Games: The Chain Store Paradox279Stationarity291Retrospective Voting and Electoral Control293Ch. 10Conclusion: Where Do We Go from Here?302How Do Formal Models Increase Our Knowledge?302The Weaknesses of Game Theory305How Does One Build a Model?311Appendix 1: Basic Mathematical Knowledge315Algebra315Set Theory318Relations and Functions320Probability Theory320Limits322Differential Calculus323Partial Derivatives and Lagrange Multipliers327Integral Calculus329The Idea of a Mathematical Proof331Appendix 2: Answers to Selected Problems333Notes345Glossary of Terms in Game Theory349Bibliography355Index365

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

Review :
"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