Game Theory for Political Scientists. James D. Morrow

Transcription

1 Game Theory for Political Scientists James D. Morrow Princeton University Press Princeton, New Jersey

2 CONTENTS List of Figures and Tables Preface and Acknowledgments xiii xix Chapter 1: Overview 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 How to Use This Book 8 The Plan of This Book 10 Further Reading 11 Textbooks; Supplementary Readings; Esoteric Books on Game Theory; Journals Chapter 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 Review 49 Further Reading 49 i

3 VIII CONTENTS Chapter 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 Review 71 Further Reading 72 Chapter 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 Review 119 Further Reading 120 Chapter 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

4 CONTENTS IX Bargaining in Legislatures 149 Why Might Backwards Induction Yield Counterintuitive Results? 156 Review. 158 Further Reading 159 In General; Legislative Studies Chapter 6: Beliefs and Perfect Bayesian Equilibria 161 Bayes's Theorem 163 The Preference for Biased Information 166 Perfect Bayesian Equilibria 170 Nuclear Deterrence 180 Review 186 Further Reading 186 In General; Comparative Politics Chapter 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 Review 216 Further Reading 217 In General; Electoral Politics Chapter 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

5 X CONTENTS An Introduction to Restrictions on Beliefs 244 "Cheap Talk" and Coordination 250 Review 256 Further Reading 257 In General; International Politics Chapter 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 Review 300 Further Reading 300 In General; Administrative Politics Chapter 10: Conclusion: Where Do We Go from Here? 302 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

6 CONTENTS XI Appendix 2: Answers to Selected Problems Notes Glossary of Terms in Game Theory Bibliography Index