Game Theory

295 Pages·2003·4.74 MB·English

GAME THEORY
Game theory is rapidly becoming established as one of the cornerstones of
the social sciences. No longer confined to economics it is spreading fast across
each of the disciplines, accompanied by claims that it represents an
opportunity to unify the social sciences by providing a foundation for a
rational theory of society.
This book is for those who are intrigued but baffled by these claims. It
scrutinises them from the perspective of the social theorist without getting lost
in the technical complexity of most introductory texts. Requiring no more
than basic arithmetic, it provides a careful and accessible introduction to the
basic pillars of game theory.
The introduction traces the intellectual origins of Game Theory and
explains its philosophical premises. The next two chapters offer a careful
exposition of the major analytical results of game theory. Whilst never losing
sight of how powerful an analytical tool game theory is, the book also points
out the intellectual limitations (as well as the philosophical and political
implications) of the assumptions it depends on. Chapter 4 turns to the theory
of bargaining, and concludes by asking: What does game theory add to the
Social Contract tradition? Chapter 5 explains the analytical significance of the
famous ‘prisoners’ dilemma’, while Chapter 6 examines how repetition of such
games can lead to particular theories of the State. Chapter 7 examines the
recent attempt to overcome theoretical dead-ends using evolutionary
approaches, which leads to some interesting ideas about social structures,
history and morality. Finally, Chapter 8 reports on laboratory experiments in
which people played the games outlined in earlier chapters.
The book offers a penetrating account of game theory, covering the main
topics in depth. However by considering the debates in and around the theory
it also establishes its connection with traditional social theories.
Shaun P.Hargreaves Heap is Dean of the School of Economic and Social
Studies, and Senior Lecturer in Economics at the University of East Anglia.
His previous books include The New Keynesian Macroeconomics (1992). Yanis
Varoufakis is Senior Lecturer in Economics at the University of Sydney. His
previous books include Rational Conflict (1991).

GAME THEORY

A Critical Introduction
Shaun P.Hargreaves Heap and
Yanis Varoufakis
London and New York
First published 1995
by Routledge
11 New Fetter Lane, London EC4P 4EE

Simultaneously published in the USA and Canada
by Routledge
29 West 35th Street, New York, NY 10001

Routledge is an imprint of the Taylor & Francis Group
This edition published in the Taylor & Francis e-Library, 2003.

© 1995 Shaun P.Hargreaves Heap and Yanis Varoufakis
All rights reserved. No part of this book may be reprinted or
reproduced or utilized in any form or by any electronic,
mechanical, or other means, now known or hereafter
invented, including photocopying and recording, or in any
information storage or retrieval system, without permission in
writing from the publishers.

British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library

Library of Congress Cataloguing in Publication Data
A catalogue record for this book is available from the Library of Congress
ISBN 0-203-19927-8 Master e-book ISBN
ISBN 0-203-19930-8 (Adobe eReader Format)
ISBN 0-415-09402-X (hbk)
ISBN 0-415-09403-8 (pbk)
CONTENTS
List of boxes viii
Preface xi
1 AN OVERVIEW 1
1.1 Introduction 1
1.2 The assumptions of game theory 4
1.3 Liberal individualism, the State and game theory 31
1.4 A guide to the rest of the book 35
1.5 Conclusion 39
2 THE ELEMENTS OF GAME THEORY 41
2.1 Introduction 41
2.2 The representation of games and some notation 42
2.3 Dominance and equilibrium 43
2.4 Rationalisable beliefs and actions 45
2.5 Nash strategies and Nash equilibrium solutions 51
2.6 Games of incomplete information 62
2.7 Trembling hands and quivering souls 64
2.8 Conclusion 79
3 DYNAMIC GAMES: BACKWARD INDUCTION AND
SOME EXTENSIVE FORM REFINEMENTS OF THE
NASH EQUILIBRIUM 80
3.1 Introduction 80
3.2 Dynamic games, the extensive form and backward induction 81
3.3 Subgame perfection 82
3.4 Backward induction, ‘out of equilibrium’ beliefs and common knowledge
instrumental rationality (CKR) 87
3.5 Sequential equilibria 93
3.6 Proper equilibria, further refinements and forward induction 97
3.7 Conclusion 100
v
CONTENTS
4 BARGAINING GAMES 111
4.1 Introduction 111
4.2 Credible and incredible talk in simple bargaining games 115
4.3 John Nash’s generic bargaining problem and his axiomatic solution 118
4.4 Ariel Rubinstein and the bargaining process: the return of Nash
backward induction 128
4.5 Justice in political and moral philosophy 137
4.6 Conclusion 144
5 THE PRISONERS’ DILEMMA 146
5.1 Introduction: the dilemma and the State 146
5.2 Examples of hidden prisoners’ dilemmas in social life 149
5.3 Kant and morality: is it rational to defect? 155
5.4 Wittgenstein and norms: is it really rational to defect? 157
5.5 Gauthier: is it instrumentally rational to defect? 162
5.6 Tit-for-tat in Axelrod’s tournaments 164
5.7 Conclusion 166
6 REPEATED GAMES AND REPUTATIONS 167
6.1 Introduction 167
6.2 The finitely repeated prisoners’ dilemma 168
6.3 The Folk theorem and the indefinitely repeated prisoners’ dilemma 170
6.4 Indefinitely repeated free rider games 175
6.5 Reputation in finitely repeated games 178
6.6 Signalling behaviour 190
6.7 Repetition, stability and a final word on the Nash equilibrium concept 192
6.8 Conclusion 194
7 EVOLUTIONARY GAMES 195
7.1 Introduction: spontaneous order versus political rationalism 195
7.2 Evolutionary stability 197
7.3 Some inferences from the evolutionary play of the hawk-dove game 202
7.4 Coordination games 214
7.5 The evolution of cooperation in the prisoners’ dilemma 218
7.6 Power, morality and history: Hume and Marx on social evolution 221
7.7 Conclusion 233
8 WATCHING PEOPLE PLAY GAMES: SOME
EXPERIMENTAL EVIDENCE 236
8.1 Introduction 236
8.2 Backward induction 238
8.3 Repeated prisoners’ dilemmas 240
8.4 Coordination games 242
8.5 Bargaining games 246
8.6 Hawk-dove games and the evolution of social roles 251
8.7 Conclusion 258
vi
CONTENTS
Postscript 260
Notes 261
Bibliography 265
Name index 273
Subject index 276
vii
LIST OF BOXES
1.1 Utility maximisation and consistent choice 6
1.2 Reflections on instrumental rationality 7
1.3 Consistent choice under risk and expected utility maximisation 10
1.4 The Allais paradox 13
1.5 Kant’s categorical imperative 16
1.6 Bayes’s rule 19
1.7 The Ellsberg paradox, uncertainty, probability assessments,
and confidence 22
1.8 Robert Aumann’s defence of the assumption of a consistent
alignment of beliefs 26
2.1 A brief history of game theory 49
2.2 Cournot’s oligopoly theory in the light of game theory 54
2.3 Agreeing to disagree even when it is costly 61
2.4 Mixed strategies 71
3.1 Blending desires and beliefs 104
3.2 Modernity under a cloud: living in a post-modern world 107
3.3 Functional explanations 109
4.1 Property rights and sparky trains 112
4.2 Marxist and feminist approaches to the State 114
4.3 Utility functions and risk aversion 119
4.4 Some violations of Nash’s axioms 126
4.5 Behind the veil of ignorance 140
5.1 Tosca’s dilemma 147
5.2 The struggle over the working day 153
5.3 The paradox of underconsumption 154
5.4 Adam Smith’s moral sentiments 157
5.5 The propensity ‘to barter, truck and exchange’ 161
5.6 Ulysses and the Sirens 163
viii
LIST OF BOXES
6.1 Cooperation in small groups and the optimal size of a group 173
6.2 The power of prophecy 177
6.3 Small doubts and lame duck Presidents 187
6.4 Self-fulfilling sexist beliefs and low pay for women 191
7.1 Winning and losing streaks? 203
7.2 Prominence and focal points in social life 205
7.3 Eating dinner 207
7.4 Coordination among MBA students 216
7.5 QWERTY and other coordination failures 217
7.6 Who gets the best jobs in West Virginia? 226
8.1 Who do you trust? 237
8.2 The curse of economics 241
8.3 Degrees of common knowledge in the laboratory 243
8.4 Athens and the Melians 257
ix