Political Game Theory - Princeton University
Political Game Theory
Nolan McCarty Adam Meirowitz
To Liz, Janis, Lachlan, and Delaney.
Contents
Acknowledgements
vii
Chapter 1. Introduction
1
1. Organization of the Book
2
Chapter 2. The Theory of Choice
5
1. Finite Sets of Actions and Outcomes
6
2. Continuous Outcome Spaces*
10
3. Utility Theory
17
4. Utility representations on Continuous Outcome Spaces* 18
5. Spatial Preferences
19
6. Exercises
21
Chapter 3. Choice Under Uncertainty
23
1. The Finite Case
23
2. Risk Preferences
32
3. Learning
37
4. Critiques of Expected Utility Theory
41
5. Time Preferences
46
6. Exercises
50
Chapter 4. Social Choice Theory
53
1. The Open Search
53
2. Preference Aggregation Rules
55
3. Collective Choice
61
4. Manipulation of Choice Functions
66
5. Exercises
69
Chapter 5. Games in the Normal Form
71
1. The Normal Form
73
2. Solutions to Normal Form Games
76
3. Application: The Hotelling Model of Political Competition 83
4. Existence of Nash Equilibria
86
5. Pure Strategy Nash Equilibria in Non-Finite Games*
93
6. Application: Interest Group Contributions
95
7. Application: International Externalities
96
iii
iv
CONTENTS
8. Computing Equilibria with Constrained Optimization*
97
9. Proving the Existence of Nash Equilibria**
98
10. Strategic Complementarity
102
11. Supermodularity and Monotone Comparative Statics* 103
12. Refining Nash Equilibria
108
13. Application: Private Provision of Public Goods
109
14. Exercises
113
Chapter 6. Bayesian Games in the Normal Form
115
1. Formal Definitions
117
2. Application: Trade restrictions
119
3. Application: Jury Voting
121
4. Application: Jury Voting with a Continuum of Signals* 123
5. Application: Public Goods and Incomplete Information 126
6. Application: Electoral Competition under Uncertainty 127
7. Application: Campaigns, Contests and Auctions*
131
8. Existence of Bayesian Nash equilibria*
133
9. Exercises
134
Chapter 7. Extensive Form Games
135
1. Backward Induction
138
2. Dynamic Games of Complete but Imperfect Information 140
3. Subgame Perfection and Perfect Equilibria
144
4. Applications
145
5. Exercises
158
Chapter 8. Dynamic Games of Incomplete Information
161
1. Perfect Bayesian Equilibria
163
2. Application: Entry Deterrence in Elections
172
3. Application: Information and Legislative Organization 178
4. Application: Informational Lobbying
183
5. Refinements of Perfect Bayesian Equilibrium*
186
6. Exercises
195
Chapter 9. Repeated Games
199
1. The Repeated Prisoner's Dilemma
200
2. The Grim Trigger Equilibrium
202
3. Tit-for-Tat Strategies
203
4. Intermediate Punishment Strategies
204
5. The Folk Theorem*
206
6. Application: Interethnic Cooperation
208
7. Application: Trade Wars
213
8. Exercises
215
CONTENTS
v
Chapter 10. Bargaining Theory
217
1. The Nash Bargaining Solution
217
2. Non-cooperative Bargaining
222
3. Majority Rule Bargaining Under Closed Rule
226
4. Bargaining with Incomplete Information
234
5. Application: Veto Bargaining
235
6. Application: Crisis Bargaining
244
7. Exercises
254
Chapter 11. Mechanism Design and Agency Theory
257
1. The Mechanism Design Problem
260
2. Applications
263
3. Incentive Compatibility and Individual Rationality
274
4. Constrained Mechanism Design
276
5. Mechanism Design and Signaling Games
291
6. Exercises
295
Chapter 12. Mathematical Appendix
299
1. Sets and Functions
301
2. The Real Number System
304
3. Points and sets
306
4. Continuity of Functions
308
5. Correspondences*
310
6. Calculus
311
7. Probability Theory
324
Bibliography
335
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