Game Theory: A Critical Introduction

Game theory now provides the theoretical underpinning for a multitude of courses in economics worldwide. The speed of these developments has been remarkable and they have constituted something of a revolution. Indeed, the basic tenets of game theory have now begun to colonize other social sciences and its proponents have been unified in claiming its natural basis as a rational theory of society. But the technical demands of the subject and the lack of clarity of many commentators' explanations have been a problem for many. This second edition of Shaun Hargreaves-Heap and Yanis Varoufakis's classic text strips away the mystique and lets the student make his or her own mind up. This new edition: * lays bear the philosophy behind game theory and explains all its major concepts * conducts a clear explanation and careful analysis of all the main 'games', such as repeated games and the prisoner's dilemma, as well as less well-trodden topics such as experimental games and issues ofrationality * introduces and analyses new areas of game theory such as "evolutionary games" and "Psychological games" Retaining the most popular features from the original edition, this latest version offers improved pedagogy, new questions for discussion, new chapters on the latest developments as well as a host of new examples. A new generation of students of game theory will grow to appreciate this superb text whilst fans of the first edition will eagerly devour this long-awaited update.

Shaun P. Hargreaves Heap is Professor of Economics at the University of East Anglia, UK.

List of boxes

xi

Preface

xiii

Overview

1

(40)

Introduction

1

(6)

Why study game theory?

1

(1)

What is game theory?

2

(1)

Why this book?

3

(1)

Why a second book?

4

(2)

The rest of this chapter

6

(1)

The assumptions of game theory

7

(26)

Individual action is instrumentally rational

7

(20)

Common knowledge of rationality (CKR)

27

(1)

Common priors

28

(3)

Action within the rules of the games

31

(2)

Liberal individualism, the state and game theory

33

(3)

Methodological individualism

33

(2)

Game theory's contribution to liberal individualism

35

(1)

A guide to the rest of the book

36

(4)

Three classic games: Hawk--Dove, Co-ordination and the Prisoner's Dilemma

36

(2)

Chapter-by-chapter guide

38

(2)

Conclusion

40

(1)

The Elements of Game Theory

41

(39)

Introduction

41

(3)

The representation of strategies, games and information sets

44

(3)

Pure and mixed strategies

44

(1)

The normal form, the extensive form and the information set

45

(2)

Dominance reasoning

47

(5)

Rationalisable beliefs and actions

52

(6)

The successive elimination of strategically inferior moves

52

(4)

Rationalisable strategies and their connection with Nash's equilibrium

56

(2)

Nash equilibrium

58

(10)

John Nash's beautiful idea

58

(2)

Consistently aligned beliefs, the hidden Principle of Rational Determinacy and the Harsanyi--Aumann doctrine

60

(1)

Some objections to Nash: Part I

61

(7)

Nash equilibrium in mixed strategies

68

(10)

The scope and derivation of Nash equilibria in mixed strategies

68

(5)

The reliance of NEMS on CAB and the Harsanyi doctrine

73

(2)

Aumann's defence of CAB and NEMS

75

(3)

Conclusion

78

(2)

Problems

79

(1)

Battling Indeterminacy: Refinements of Nash's Equilibrium in Static and Dynamic Games

80

(47)

Introduction

80

(1)

The stability of Nash equilibria

81

(9)

Trembling hand perfect Nash equilibria

81

(4)

Harsanyi's Bayesian Nash equilibria and his defence of NEMS

85

(5)

Dynamic games

90

(16)

Extensive form and backward induction

90

(2)

Subgame perfection, Nash and CKR

92

(4)

Sequential equilibria

96

(3)

Bayesian learning, sequential equilibrium and the importance of reputation

99

(4)

Signalling equilibria

103

(3)

Further refinements

106

(5)

Proper equilibria

106

(2)

Forward induction

108

(3)

Some logical objections to Nash, Part II

111

(7)

A critique of subgame perfection

111

(3)

A negative rejoinder (based on the Harsanyi--Aumann doctrine)

114

(1)

A positive rejoinder (based on sequential equilibrium)

115

(2)

Summary: out-of-equilibrium beliefs, patterned trembles and consistency

117

(1)

Conclusion

118

(9)

The status of Nash and Nash refinements

118

(1)

In defence of Nash

119

(3)

Why has game theory been attracted `so uncritically' to Nash?

122

(3)

Problems

125

(2)

Bargaining Games: Rational Agreements, Bargaining Power and the Social Contract

127

(45)

Introduction

127

(4)

Credible and incredible talk in simple bargaining games

131

(4)

John Nash's generic bargaining problem and his axiomatic solution

135

(15)

The bargaining problem

135

(2)

Nash's solution -- an example

137

(3)

Nash's solution as an equilibrium of fear

140

(6)

Nash's axiomatic account

146

(2)

Do the axioms apply?

148

(2)

Ariel Rubinstein and the bargaining process: the return of Nash backward induction

150

(14)

Rubinstein's solution to the bargaining problem

150

(2)

A proof of Rubinstein's theorem

152

(8)

The (trembling hand) defence of Rubinstein's solution

160

(3)

A final word on Nash, trembling hands and Rubinstein's bargaining solution

163

(1)

Justice in political and moral philosophy

164

(6)

The negative result and the opening to Rawls and Nozick

165

(3)

Procedures and outcomes (or `means' and ends) and axiomatic bargaining theory

168

(2)

Conclusion

170

(2)

Problems

171

(1)

The Prisoner's Dilemma: The Riddle of Co-Operation and Its Implications For Collective Agency

172

(39)

Introduction: the state and the game that popularised game theory

172

(3)

Examples of hidden Prisoner's Dilemmas and free riders in social life

175

(5)

Some evidence on how people play the Prisoner's Dilemma and free rider games

180

(5)

Explaining co-operation

185

(6)

Kant and morality: is it rational to defect?

185

(1)

Altruism

186

(1)

Inequality aversion

187

(2)

Choosing a co-operative disposition instrumentally

189

(2)

Conditional co-operation in repeated Prisoner's Dilemmas

191

(14)

Tit-for-Tat in Axelrod's tournament

191

(1)

Tit-for-Tat as a Nash equilibrium strategy when the horizon is unknown

192

(2)

Spontaneous public good provision

194

(2)

The Folk Theorem and Indeterminacy in indefinitely repeated games

196

(6)

Does a finite horizon wreck co-operation? The theory and the evidence

202

(3)

Conclusion: co-operation and the State in Liberal theory

205

(6)

Rational co-operation?

205

(1)

The debate in Liberal political theory

206

(3)

The limits of the Prisoner's Dilemma

209

(1)

Problems

209

(2)

Evolutionary Games: Evolution, Games and Social Theory

211

(56)

Introduction

211

(9)

The origins of Evolutionary Game Theory

212

(2)

Evolutionary stability and equilibrium: an introduction

214

(6)

Symmetrical evolution in homogeneous populations

220

(7)

Static games

220

(3)

Dynamic games

223

(4)

Evolution in heterogeneous populations

227

(21)

Asymmetrical (or two-dimensional) evolution and the demise of Nash equilibria in mixed strategies

227

(5)

Does Evolutionary Game Theory apply to humans as well as it does to birds, ants, etc.? An experiment with two-dimensional evolution in the Hawk-Dove game

232

(4)

Multi-dimensional evolution and the conflict of conventions

236

(5)

The origin of conventions and the challenge to methodological individualism

241

(4)

The politics of mutations: conventions, inequality and revolt

245

(2)

Discriminatory conventions: a brief synopsis

247

(1)

Social evolution: power, morality and history

248

(16)

Social versus natural selection

248

(3)

Conventions as covert social power

251

(1)

The evolution of predictions into moral beliefs: Hume on morality

252

(3)

Gender, class and functionalism

255

(3)

The evolution of predictions into ideology: Marx against morality

258

(6)

Conclusion

264

(3)

Problems

266

(1)

Psychological Games: Demolishing the Divide Between Motives and Beliefs

267

(35)

Introduction

267

(1)

Different types of `other regarding' motives

268

(7)

The `other' regarding motives of Homo Economicus

268

(1)

Beliefs as predictions and as motives

269

(6)

The power of normative beliefs

275

(17)

Fairness equilibria

275

(6)

Computing fairness equilibria

281

(2)

An assessment of Rabin

283

(2)

An alternative formulation linking entitlements to intentions

285

(4)

Team thinking

289

(3)

Psychology and evolution

292

(7)

On the origins of normative beliefs: an adaptation to experience

292

(1)

On the origins of normative beliefs: the resentment-aversion versus the subversion-proclivity hypotheses

293

(6)

Conclusion: shared praxes, shared meanings

299

(3)

Problems

301

(1)

Postscript

302

(2)

Answers to problems

304

(30)

Notes

334

(14)

Bibliography

348

(11)

Name index

359

(3)

Subject index

362

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Game Theory: A Critical Introduction

Summary

Author Biography

Table of Contents

Supplemental Materials