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Preface and Acknowledgments Chapter 1: Overview What Is Game Theory? What Can You Do with Game Theory? Four Problems in Political Science Why Model? The Rational Choice Approach to Social Modeling How to Use This Book The Plan of This Book Chapter 2: Utility Theory The Concept of Rationality How Do Utility Functions Predict Actions? An Example: Nixon's Christmas Bombing Certainty, Risk, and Uncertainty Utility Theory under the Condition of Risk Some Common Misconceptions about Utility Theory Utility Functions and Types of Preferences A Simple Example: The Calculus of Deterrence Another Simple Example: The Decision to Vote Why Might Utility Theory Not Work? Chapter 3: Specifying a Game Formalizing a Situation: Deterrence in the Cuban Missile Crisis Games in Extensive Form Games in Strategic Form Chapter 4: Classical Game Theory Defining the Terms of Classical Game Theory Domination, Best Replies, and Equilibrium Mixed Strategies The Minmax Theorem and Equilibria of Two-Person, Zero-Sum Games Characteristics of Nash Equilibria Nash Equilibria and Common Conjectures Rationalizability Political Reform in Democracies Candidate Competition in the Spatial Model of Elections A Very Brief Introduction to Cooperative Game Theory Chapter 5: Solving Extensive-Form Games: Backwards Induction and Subgame Perfection Backwards Induction Subgame Perfection Sophisticated Voting
Agenda Control Legislative Rules and Structure-Induced Equilibria The Rubinstein Bargaining Model Bargaining in Legislatures Why Might Backwards Induction Vield Counterintuitive Results? Chapter 6: Beliefs and Perfect Bayesian Equilibrig Bayes's Theorem The Preference for Biased Information Perfect Bayesian Equilibria Nuclear Deterrence Chapter 7: More on Noncooperative Equilibrium: Perfect and Sequential Equilibria Elimination of Weakly Dominated Strategies Perfect Equilibrium Sequential Equilibrium Deterrence and the Signaling of Resolve "Why Vote?" Redux Chapter 8: Games of Limited Information and Restrictions on Beliefs Signaling Games The Informational Role of Congressional Committees Bargaining under Incomplete Information Deterrence and Out-of-Equilibrium Beliefs An Introduction to Restrictions on Beliefs "Cheap Talk" and Coordination Review Further Reading In General; International Politics Chapter 9: Repeated Games Thinking about Repetition: Iterated Prisoner's Dilemma Folk Theorems Finite Repeated Games: The Chain Store Paradox Stationarity Retrospective Voting and Electoral Control Chapter 10: Conclusion: Where Do We Go from Here? How Do Formal Models Increase Our Knowledge? The Weaknesses of Game Theory How Does One Build a Model? Further Reading Appendix 1: Basic Mathematical Knowledge Algebra Set Theory Relations and Functions Probability Theory Limits Differential Calculus Partial Derivatives and Lagrange Multipliers Integral Calculus The Idea of a Mathematical Proof Appendix 2: Answers to Selected Problems Notes Glossary of Terms in Game Theory Bibliography Index