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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