Bargaining Theory with Applications

373 Pages·1999·7.835 MB·English

by  Abhinay Muthoo

Bargaining Theory with Applications
The first unified and systematic treatment of the modern theory of bargain-
ing, presented together with many examples of how that theory is applied
in a variety of bargaining situations.
Abhinay Muthoo provides a masterful synthesis of the fundamental re-
sults and insights obtained from the wide-ranging and diverse (game theo-
retic) bargaining theory literature. Furthermore, he develops new analyses
and results, especially on the relative impacts of two or more forces on the
bargaining outcome. Many topics — such as inside options, commitment
tactics and repeated bargaining situations — receive their most extensive
treatment to date. In the concluding chapter, he offers pointers towards
future research.
Bargaining Theory with Applications is a textbook for graduate students
in economic theory and other social sciences and a research resource for
scholars interested in bargaining situations.
Abhinay Muthoo is Professor of Economics at the University of Essex. He
was educated at the London School of Economics and the University of Cam-
bridge. Professor Muthoo has published papers on bargaining theory and
game theory, among other topics, in journals such as Review of Economic
Studies, Journal of Economic Theory, Games and Economic Behavior and
Economic Journal.

Bargaining Theory
with Applications
ABHINAY MUTHOO
University of Essex
CAMBRIDGE
UNIVERSITY PRESS
PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE
The Pitt Building, Trumpington Street, Cambridge, United Kingdom
CAMBRIDGE UNIVERSITY PRESS
The Edinburgh Building, Cambridge CB2 2RU, UK
40 West 20th Street, New York, NY 10011-4211, USA
477 Williamstown Road, Port Melbourne, VIC 3207, Australia
Ruiz de Alarcon 13, 28014 Madrid, Spain
Dock House, The Waterfront, Cape Town 8001, South Africa
http://www.cambridge.org
© Abhinay Muthoo 1999
This book is in copyright. Subject to statutory exception
and to the provision of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.
First Published 1999
Reprinted 2002
Typeface Computer Modern llpt. System ET^X2e [Typeset by the author]
A catalogue record for this book is available from the British Library
Library of Congress Cataloguing in Publication data applied for
ISBN 0 521 572258 hardback
ISBN 0 521 576474 paperback
Transferred to digital printing 2004
To my parents

Contents
Preface xiii
1 Preliminaries 1
1.1 Bargaining Situations and Bargaining 1
1.2 Outline of the Book 3
1.3 The Role of Game Theory 6
1.4 Further Remarks 6
2 The Nash Bargaining Solution 9
2.1 Introduction 9
2.2 Bargaining over the Partition of a Cake 10
2.2.1 Characterization 12
2.2.2 Examples 15
2.3 Applications 16
2.3.1 Bribery and the Control of Crime 16
2.3.2 Optimal Asset Ownership 17
2.4 A General Definition 22
2.4.1 Characterization 24
2.5 Applications 25
2.5.1 Union-Firm Negotiations 25
2.5.2 Moral Hazard in Teams 27
viii Contents
2.5.3 Bribery and the Control of Crime: An Extension 29
2.6 Axiomatic Foundation 30
2.7 An Interpretation 33
2.8 Asymmetric Nash Bargaining Solutions 35
2.9 Appendix: Proofs 37
2.10 Notes 39
3 The Rubinstein Model 41
3.1 Introduction 41
3.2 The Basic Alternating-Offers Model 42
3.2.1 The Unique Subgame Perfect Equilibrium 43
3.2.2 Proof of Theorem 3.1 47
3.2.3 Properties of the Equilibrium 50
3.2.4 The Value and Interpretation of the Alternating-Offers
Model 53
3.3 An Application to Bilateral Monopoly 55
3.4 A General Model 59
3.4.1 The Subgame Perfect Equilibria 60
3.4.2 Small Time Intervals 64
3.4.3 Relationship with Nash's Bargaining Solution 65
3.4.4 Proof of Theorems 3.2 and 3.3 67
3.5 An Application to a Two-Person Exchange Economy 69
3.6 Notes 71
4 Risk of Breakdown 73
4.1 Introduction 73
4.2 A Model with a Risk of Breakdown 74
4.2.1 The Unique SPE when both Players are Risk Neutral 75
4.2.2 The Unique SPE with Risk Averse Players 77
4.3 An Application to Corruption in Tax Collection 81
4.4 The Effect of Discounting 85
4.4.1 Small Time Intervals 87
4.4.2 Risk Neutral Players: Split-The-Difference Rule 89
4.5 An Application to Price Determination 91
4.6 A Generalization 95
4.7 Notes 96
Contents ix
5 Outside Options 99
5.1 Introduction 99
5.2 A Model with Outside Options 100
5.2.1 Relationship with Nash's Bargaining Solution 104
5.3 Applications 105
5.3.1 Relationship-Specific Investments 105
5.3.2 Sovereign Debt Negotiations 107
5.3.3 Bribery and the Control of Crime Revisited 109
5.4 The Effect of a Risk of Breakdown 110
5.4.1 The Unique Subgame Perfect Equilibrium 111
5.4.2 Relationship with Nash's Bargaining Solution 113
5.4.3 The Impact of The Manner of Disagreement 114
5.4.4 A Generalization 115
5.5 Searching for Outside Options 116
5.5.1 Searching on the Streets 118
5.5.2 Searching while Bargaining 121
5.6 The Role of the Communication Technology 124
5.6.1 Equilibria in the Telephone Game 125
5.6.2 An Application to Relationship-Specific Investments 130
5.6.3 Rubinstein Bargaining with Quit Options 131
5.7 Appendix: Proofs 133
5.8 Notes 135
6 Inside Options 137
6.1 Introduction 137
6.2 A Model with Inside Options 138
6.3 Applications 143
6.3.1 Takeovers in a Duopolistic Market 143
6.3.2 Sovereign Debt Renegotiations 144
6.4 The Effect of Outside Options 146
6.4.1 And a Risk of Breakdown 149
6.4.2 Relationship with Nash's Bargaining Solution 151
6.4.3 A Generalization 152
6.5 An Application to Intrafamily Allocation 154
6.6 Endogenously Determined Inside Options 158
6.6.1 Stationary Equilibria 159
x Contents
6.6.2 Markov Equilibria 160
6.6.3 Uniqueness of SPE and Non-Markov Equilibria 165
6.7 An Application to Wage Renegotiations 170
6.7.1 Multiple Pareto-Efficient Equilibria 171
6.7.2 Equilibria with Strikes 173
6.8 Appendix: Proofs 174
6.9 Notes 185
7 Procedures 187
7.1 Introduction 187
7.2 Who Makes Offers and When 188
7.2.1 The Ultimatum Game 189
7.2.2 Repeated Offers 190
7.2.3 Simultaneous Offers 191
7.2.4 Random Proposers 192
7.2.5 Alternating-Offers with Different Response Times 193
7.3 The Effect of Retractable Offers 194
7.3.1 A Subgame Perfect Equilibrium 195
7.3.2 On the Uniqueness of the Equilibrium 195
7.3.3 Multiple Equilibria and Delay 197
7.3.4 Discussion and Interpretation 198
7.4 Burning Money: A Tactical Move 200
7.4.1 A Subgame Perfect Equilibrium 201
7.4.2 On the Uniqueness of the Equilibrium 201
7.4.3 Multiple Equilibria 202
7.4.4 Equilibrium Delay 204
7.4.5 Discussion 208
7.4.6 An Application to Surplus Destruction 208
7.5 Notes 209
8 Commitment Tactics 211
8.1 Introduction 211
8.2 The Basic Model 214
8.2.1 The Formal Structure 214
8.2.2 Interpretation 217
8.2.3 The Equilibrium 218