Game Theory and Political Theory: An

This book integrates political theory and mathematical models of political and economic processes.

Preface

ix

Acknowledgments

xv

Individual preference and individual choice

1

(52)

Some fundamental notation and definitions

2

(8)

Actions

3

(1)

Outcomes

4

(5)

States of nature

9

(1)

Preferences

10

(6)

The preference relation

12

(1)

Ordinal utility

13

(3)

Multiattribute outcomes

16

(12)

Decision making under certainty

28

(9)

Constrained economic decisions

29

(3)

Constrained political decisions

32

(5)

Decision making under risk

37

(5)

The meaning of cardinal utility

42

(6)

Cardinal utility and subjective probability

48

(3)

Allais's paradox

48

(1)

The calculus of voting

49

(2)

Summary

51

(2)

Individual preference and social choice

53

(44)

Arrow's impossibility result

56

(9)

Paradoxes of voting

65

(6)

The agenda paradox

65

(1)

The contrived Condorcet paradox

66

(1)

The dominated-winner paradox

67

(1)

The inverted-order paradox

68

(1)

The winner-turns-loser paradox

69

(1)

The truncated point-total paradox

70

(1)

The majority-winner paradox

70

(1)

The power of agendas

71

(11)

Misrepresentation of preferences

82

(7)

Vote trading

89

(5)

Summary

94

(3)

Basic theory of noncooperative games

97

(47)

Noncooperative games: an example

98

(1)

Games in extensive form: the game tree

99

(7)

Strategy and the normal form

106

(6)

Normal form of infinite games

112

(2)

Best-response strategies and domination

114

(3)

Pure-strategy equilibria

117

(3)

Some conditions for existence of pure-strategy equilibria

120

(13)

Games of perfect information

120

(1)

Some simple voting games

121

(6)

Concave---convex games and the fundamental theorem

127

(6)

Mixed strategies

133

(4)

Perfect equilibria

137

(5)

Summary

142

(2)

Elections and two-person zero-sum games

144

(59)

Zero-sum games

144

(2)

Interchangeability and equivalence

146

(3)

Maxmin and minmax

149

(5)

Concave games and resource allocations in elections

154

(4)

Symmetric games and candidate objectives

158

(2)

Two-candidate elections with a single issue

160

(6)

Two-candidate multidimensional elections

166

(9)

Disequilibrium with income redistribution policies

175

(5)

Mixed strategies and the uncovered set in elections

180

(7)

Rational expectations and voter ignorance

187

(9)

N-person zero-sum games

196

(4)

Summary

200

(3)

Nonzero-sum games: political economy, public goods, and the prisoners' dilemma

203

(40)

Nonzero-sum games

203

(3)

The two-person prisoners' dilemma

206

(4)

Public goods and externalities

210

(5)

An analogous game with a continuum of strategies

215

(5)

Other prisoners' dilemmas

220

(15)

Arms races

221

(1)

Interest groups and collective action

222

(3)

Political participation

225

(8)

Vote trading

233

(2)

Demand-revealing mechanisms

235

(6)

Summary

241

(2)

Institutions, strategic voting, and agendas

243

(59)

Sincere voting, issue by issue

245

(12)

Sophisticated voting, issue by issue

257

(6)

The disappearance of stability without separability

263

(3)

Sophisticated voting and agendas

266

(18)

Binary agendas

267

(4)

Amendment agendas

271

(10)

Congressional agendas

281

(2)

Partially sophisticated committees

283

(1)

Some experimental and empirical evidence

284

(7)

Incomplete information and sophisticated voting

291

(7)

Summary

298

(4)

Cooperative games and the characteristic function

302

(37)

Strong equilibria

304

(2)

The characteristic function, v(C)

306

(7)

Simple games

313

(4)

The special case of transferable utility

317

(5)

Some examples of characteristic-function games

322

(8)

The valley of the dump

322

(1)

Normalized games

322

(3)

Market games

325

(1)

Pollution, externalities, and the prisoners' dilemma

325

(5)

Alternative forms of v(C)

330

(2)

Ambiguities in v(C)

332

(5)

Summary

337

(2)

The core

339

(48)

The core

340

(5)

The core and Pareto-optimality

345

(4)

Transferable utility games

349

(6)

Transferable utility and the core

349

(4)

The Coase theorem

353

(2)

Balanced games

355

(6)

A necessary and sufficient condition for existence

355

(2)

Market games

357

(4)

Committees with a single issue

361

(3)

An extended example: the Genossenschaften

364

(6)

Multiple dimensions and some experimental evidence

370

(6)

Logrolling and some experimental ambiguities

376

(2)

Extraordinary majorities

378

(4)

The core and ambiguities with v(C)

382

(2)

Summary

384

(3)

Solution theory

387

(54)

The stable set

389

(4)

Some properties of V-sets

393

(5)

Relationship of V to the core

393

(1)

Existence and uniqueness of V

394

(4)

Bargaining sets for simple voting games

398

(4)

Cooperative vs. noncooperative analysis of committees

402

(2)

Extensions of the bargaining set

404

(4)

The size principle

408

(6)

Problems with nontransferable utility games

414

(4)

The competitive solution

418

(8)

Some experimental evidence

426

(8)

Spatial committees

426

(1)

Weighted voting systems

427

(4)

Vote trading

431

(1)

Experimental anomalies

432

(2)

A noncooperative view and alternative ideas

434

(3)

Summary

437

(4)

Repeated games and information: some research frontiers

441

(44)

The repeated prisoners' dilemma

442

(6)

The balance of power

448

(3)

A finitely repeated game: the chain store paradox

451

(11)

The Shapley value and the power index

462

(8)

The Nash bargaining model

470

(5)

Relating the Shapley value to Nash's scheme

475

(3)

Reciprocity and repeated games

478

(5)

Summary

483

(2)

References and a guide to the literature

485

(16)

Index

501

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Game Theory and Political Theory: An Introduction

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Table of Contents

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