Game Theory and Politics

This illuminating and instructive survey demonstrates both the insights and the pitfalls that result from applying game theoretic models to the analysis of problems in political science. Using real-life examples, it shows how game theory can explain and elucidate complex political situations, from warfare to presidential vetoes. 1975 edition. 24 figures.

Preface to the Dover Edition

ix

Preface

xi

Introductory Note

xv

List of Tables

xvii

List of Figures

xix

International Relations Games

1

(50)

Introduction

1

(1)

Two-Person Zero-Sum Games with Saddlepoints

2

(6)

Information in Games

8

(5)

Two-Person Zero-Sum Games without Saddlepoints

13

(4)

Pure and Mixed Strategies

17

(3)

Interpretation of Mixed Strategies

20

(6)

Two-Person Nonzero-Sum Games

26

(4)

Prisoner's Dilemma and the Theory of Metagames

30

(9)

Chicken and the Cuban Missile Crisis

39

(8)

Summary and Conclusion

47

(4)

Qualitative Voting Games

51

(50)

Introduction

51

(1)

Voting Procedures

52

(4)

Sincere Voting

56

(4)

Straightforward Strategies and Voting Procedures

60

(3)

Equilibrium Choices and Vulnerability

63

(4)

Desirable Strategies and Equilibria

67

(2)

The Relationship between Desirable and Admissible Strategies

69

(4)

Sophisticated Voting

73

(5)

Coalitions and Information

78

(4)

Voting on Voting Procedures

82

(3)

The Paradox of Voting

85

(3)

Empirical Examples

88

(8)

Summary and Conclusion

96

(5)

Quantitative Voting Games

101

(24)

Introduction

101

(1)

Requirements for a Voting System of Proportional Representation

102

(2)

Rules that Meet the Requirements

104

(2)

Interdependence of the Requirements

106

(2)

The Effects of Size

108

(3)

Information and the Choice of Strategies

111

(5)

Empirical Examples

116

(5)

Summary and Conclusion

121

(4)

Vote-Trading Games

125

(32)

Introduction

125

(1)

What the General Possibility Theorem Precludes

126

(3)

Judgments about Vote Trading

129

(2)

Definitions and Assumptions

131

(2)

Sincere and Insincere Voting

133

(4)

Initial Trades and the Paradox of Vote Trading

137

(3)

Subsequent Trades and the Instability of Vote Trading

140

(2)

The Consequences of Refusing to Trade

142

(2)

The Consequences of Forming Coalitions

144

(4)

Conditions Limiting Vote Trading

148

(3)

Empirical Examples of the Paradox of Vote Trading

151

(3)

Summary and Conclusion

154

(3)

Voting Power

157

(42)

Introduction

157

(1)

The Shapley-Shubik Index of Voting Power

158

(6)

The Banzhaf Index of Voting Power

164

(3)

Coalition Models of the Two Power Indices

167

(4)

Calculation of the Power Indices

171

(5)

Three Paradoxes of Voting Power

176

(6)

Empirical Applications of the Power Indices

182

(13)

Summary and Conclusion

195

(4)

Coalition Games

199

(44)

Introduction

199

(1)

Power and Coalitions

200

(2)

Restrictions on Coalition Alignments

202

(2)

The Stability of Alignments

204

(5)

Empirical Conclusions of the Luce-Rogow Model

209

(4)

The Concept of Winning

213

(3)

The Size Principle

216

(4)

The Information Effect

220

(2)

Empirical Evidence for the Size Principle

222

(4)

Criticisms of the Size Principle

226

(6)

An Alternative Goal: Maximizing One's Share of Spoils

232

(8)

Summary and Conclusion

240

(3)

Election Games

243

(36)

Introduction

243

(1)

The Need for Models to Assess the Consequences of Electoral Reform

244

(3)

Presidential Campaigns and Voting Behavior

247

(2)

The Goals of Candidates

249

(2)

The Popular-Vote Model

251

(4)

The Electoral-Vote Model

255

(2)

The 3/2's Allocation Rule

257

(3)

Why the Large States Are Favored

260

(3)

Testing the Models

263

(3)

Campaign Allocations and Biases through 1980

266

(6)

Limitations and Extensions of the Models

272

(3)

Summary and Conclusion

275

(4)

Glossary

279

(12)

Annotated Bibliography

291

(4)

Index

295

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Game Theory and Politics

Summary

Table of Contents

Supplemental Materials