Carmichael_ppr 9/19/07 5:43 PM Page 1 Almost every aspect of life presents us with decision problems, ranging from A Guide to Game Theory the simple question of whether to have pizza or ice cream, or where to aim a penalty kick, to more complex decisions like how a company should compete with others and how governments should negotiate treaties. Game theory is a technique that can be used to analyse strategic problems in diverse settings; its application is not limited to a single discipline such as economics or business studies. A Guide to Game Theory reflects this interdisciplinary potential to provide an introductory overview of the subject. Fiona Carmichael Put off by a fear of maths? No need to be, as this book explains many of the important concepts and techniques without using mathematical language or methods.
This will enable those who are alienated by maths to work with and understand many game theoretic techniques. KEY FEATURES ◆ Key concepts and techniques are introduced in early chapters, such as the prisoners’ dilemma and Nash equilibrium. Analysis is later built up in a step-by-step way in order to incorporate more interesting features of the world we live in. ◆ Using a wide range of examples and applications the book covers decision problems confronted by firms, employers, unions, footballers, partygoers, politicians, governments, non-governmental organisations and communities.
◆ Exercises and activities are embedded in the text of the chapters and A Guide to additional problems are included at the end of each chapter to test understanding. ◆ Realism is introduced into the analysis in a sequential way, enabling you to build on your knowledge and understanding and appreciate the potential uses of the theory. Game Theory Suitable for those with no prior knowledge of game theory, studying courses related to strategic thinking. Such courses may be a part of a degree Carmichael programme in business, economics, social or natural sciences.
FIONA CARMICHAEL is Senior Lecturer in Economics at the University of Salford. She has a wealth of experience in helping students tackle this potentially daunting yet fascinating subject, as recognised by an LTSN award for ‘Outstanding Teaching’ on her innovative course in game theory. An imprint of www.com Tai Lieu Chat Luong A Guide to Game Theory We work with leading authors to develop the strongest educational materials in game theory, bringing cutting-edge thinking and best learning practice to a global market. Under a range of well-known imprints, including Financial Times Prentice Hall, we craft high quality print and electronic publications which help readers to understand and apply their content, whether studying or at work.
To find out more about the complete range of our publishing, please visit us on the World Wide Web at: www.uk A Guide to Game Theory Fiona Carmichael Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.uk First published 2005 © Pearson Education Limited 2005 The right of Fiona Carmichael to be identified as author of this work has been asserted by her in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP. All trademarks used herein are the property of their respective owners.
The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners. ISBN 0 273 68496 5 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress. 10 9 8 7 6 5 4 3 2 1 08 07 06 05 04 Typeset in 9/12pt Stone Serif by 30.
Printed and bound in Great Britain by Henry Ling Ltd, at the Dorset Press, Dorchester, Dorset. The publisher’s policy is to use paper manufactured from sustainable forests. To Jessie and Rosie 1 CONTENTS Preface xi Acknowledgements xiv Publisher‘s acknowledgements xv CHAPTER 1 Game theory toolbox 1 Introduction 2 1.1 The idea of game theory 3 1.2 Describing strategic games 5 1.3 Simultaneous-move games 7 1.4 Sequential-move or dynamic games 13 1.6 Cooperative and non-cooperative games 16 1.8 Information 17 Summary 18 Answers to exercises 19 Problems 20 Questions for discussion 20 Notes 20 CHAPTER 2 Moving together 21 Introduction 22 2.1 Dominant-strategy equilibrium 22 2.2 Iterated-dominance equilibrium 29 2.4 Some classic games 43 Summary 50 Answers to exercises 5 1. Problems 53 Questions for discussion 54 viii Contents Answers to problems 55 Notes 56 CHAPTER 3 Prisoners’ dilemma 57 Introduction 58 3.1 Original prisoners’ dilemma game 58 3.2 Generalised prisoners’ dilemma 60 3.3 Prisoners’ dilemma and oligopoly collusion 62 3.5 Prisoners’ dilemma and public goods 66 3.6 Prisoners’ dilemma and open-access resources 68 3.8 Resolving the prisoners’ dilemma 71.
Summary 72 Answers to exercises 73 Problems 74 Questions for discussion 75 Answers to problems 75 Notes 76 CHAPTER 4 Taking turns 79 Introduction 80 4.1 Foreign direct investment game 81.2 Nice–not so nice game 89 4.5 Centipede games 100 Summary 103 Answers to exercises 104 Problems 105 Questions for discussion 106 Answers to problems 106 Notes 107 CHAPTER 5 Hidden moves and risky choices 109 Introduction 110.2 Risk and probabilities 113.3 Limitations of expected utility theory 125 Summary 135 Answers to exercises 136 Problems 137 Questions for discussion 137 Contents ix Answers to problems 138 Notes 139 CHAPTER 6 Mixing and evolving 141 Introduction 142 6.1 Nash equilibrium in mixed strategies 142 6.2 Evolutionary games 149 Summary 157 Answers to exercises 158 Problems 159 Questions for discussion 160 Answers to problems 161. Notes 162 CHAPTER 7 Mystery players 163 Introduction 164 7.1 Friends or enemies again 165 7.2 Entry deterrence with incomplete information 170 7.3 Entry deterrence with signalling 173 7.4 Numerical example of entry deterrence with signalling 175 7.5 The beer and quiche signalling game 178 7.6 Asymmetric information for both players in the battle of the sexes 185 Summary 189 Answers to exercises 190 Problems 191. Questions for discussion 193 Answers to problems 193 Notes 194 CHAPTER 8 Playing again and again .2 Infinite and indefinite repetition 203 8.3 Asymmetric information in the finitely repeated prisoners’ dilemma 209 8.4 Resolving the chain store paradox 216.5 Experimental evidence 225 Summary 228 Answers to exercises 229 Problem 231. Questions for discussion 232 Answer to problem 232 Notes 232 x Contents CHAPTER 9 Bargaining and negotiation 235 Introduction 236 9.1 Cooperative and non-cooperative bargaining theory 236 9.3 Cooperative bargaining theory 241.4 Non-cooperative, strategic bargaining with alternating offers 249 9.5 Experimental evidence 263 Summary 265 Answers to exercises 266 Problems 267 Questions for discussion 267 Answers to problems 268 Notes 268 Bibliography 271.
Index 279 PREFACE This book gives an introductory overview of game theory. It has been written for people who have little or no prior knowledge of the theory and want to learn a lot without getting bogged down in either thousands of examples or mathematical quicksand. Game theory is a technique that can be used to analyse strategic problems in diverse settings. Its application is not limited to a single discipline such as economics or business studies and this book reflects this interdisciplinary potential.
A wide range of examples and applications are used including decision problems confronted by firms, employers, unions, footballers, partygoers, politicians, governments, non-governmental organisa- tions and communities. Students on different social and natural sciences programmes where game theory is part of the curriculum should therefore find this book useful. It will be particularly helpful for students who sometimes feel daunted by mathematical language and expositions. I have written it with them in mind and have kept the maths to a minimum to prevent it from becoming overbearing.
Mathematical language can act as a barrier that stops theories like game theory, that have their origins in mathematics, from being applied elsewhere. This book aims to break down these barriers and the exposition relies heavily on a logical approach aided by tables and diagrams. Often this is all that is needed to convey the essential aspects of the scenario under investigation. However, this won’t always be the case and sometimes, in order to get closer to the real world, it is helpful to use mathematical language in order to give preci- sion to what might otherwise be very long and possibly rambling explanations.
In the first four chapters of this book you will learn about many of the important ideas in game theory: concepts like zero-sum games, the prisoners’ dilemma, Nash equilibrium, credible threats and more. In the subsequent chap- ters the analysis is built up in a step-by-step way in order to incorporate more of the interesting features of the world we live in, such as risk, information asymmetries, signals, long-term relationships, learning and negotiation. Naturally, the insights generated by the theory are likely to be more useful the xii Preface greater the degree of reality incorporated into the analysis. The trade-off is that the more closely the analysis mirrors the real world the more intricate it becomes.
To help you thread your way through these intricacies a small number of examples are followed through and analysed in detail. An alterna- tive approach might be to build on the material in the earlier chapters by applying it in some specific but relatively narrowly-defined circumstances. This alternative would bypass many of the potential uses of game theory and, I think, do you and the theory a disservice. As you read through the chapters in this book you will find that there are plenty of opportunities for you to put into practice the game theory you learn by working through puzzles, or more formally in the language of the class- room, exercises and problems.
The exercises are embedded in the text of the chapters and there are additional problems and discussion questions at the end of the chapters. Working through problems is a really good way of testing your understanding and you may find that learning game theory is a bit like learn- ing to swim or ride a bike in that it is something that you can only really understand by doing. The plan of this book is as follows. In Chapter 1, some of the basic ideas and concepts underlying game theory are outlined and some examples are given of the kinds of scenario where game theory can be applied usefully.
The objectives of using game theory in these circumstances are also discussed. In Chapter 2 simultaneous- or hidden-move games are analysed and the dominant strategy and Nash equilibrium concepts are defined. Some limitations of these solution concepts are also discussed. The subject of Chapter 3 is the prisoners’ dilemma, a famous hidden-move game.
In Chapter 3 you will see how the prisoners’ dilemma can be generalised and set in a variety of contexts. You will see that some important questions are raised by the prisoners’ dilemma in relation to decision theory in general and ideas of rationality in particular. Examples of prisoners’ dilemmas in the social, business and political spheres of life are explored. Some related policy ques- tions in connection with public and open access goods and the free rider effect are analysed in depth using examples.
Dynamic games are analysed in Chapter 4 and you will learn how sequential decision making can be modelled using game theory and extensive forms. Examples are used to demonstrate why the idea of a Nash equilibrium on its own may not be enough to solve dynamic games.