Negotiation games: applying game theory to bargaining and arbitration

330 Pages·2003·2.05 MB·English

by  Steven Brams

Negotiation Games
Revised Edition
The concept of Negotiation is critical to coping with all manner of
strategic problems that arise in the everyday dealings that people have
with each other and with organizations. Game theory illustrates this to
the full and shows how these problems can be solved.
This is a revised edition of a classic book and uses some wonderfully
adroit case studies that remain relevant today. Negotiation Games covers
such themes as:
• trade offs and the game of chicken
(cid:127) the effects of power in the cease-fire game
(cid:127) the use of threat power in sequential games
(cid:127) fallback bargaining and rational negotiation
Written by one of the leading game theorists of the generation, this book
will be greatly appreciated not only by academics and students involved
in game theory, economics, business and international relations, but also
by those involved in diplomacy and international business.
Routledge Advances in Game Theory
Edited by Christian Schmidt
Volume 1
Game Theory and Economic Analysis
A Quiet Revolution in Economics
Christian Schmidt
Volume 2
Negotiation Games
Applying Game Theory to Bargaining and Arbitration
Steven J.Brams
Negotiation Games
Revised Edition
Applying Game Theory to
Bargaining and Arbitration
Steven J.Brams
LONDON AND NEW YORK
First published 1990
by Routledge
29 West 35th Street, New York, NY 10001
Revised Edition first published 2003 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, 2005.
“To purchase your own copy of this or any of Taylor & Francis or Routledge’s
collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.”
© 2003 Steven J.Brams
All rights reserved. No part of this book may be reprinted or
reproduced or utilised 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 Cataloging in Publication Data
A catalog record for this book has been requested
ISBN 0-203-18042-9 Master e-book ISBN
ISBN 0-203-34423-5 (Adobe eReader Format)
ISBN 0-415-30894-1 (hbk)
ISBN 0-415-30895-X (pbk)
Contents
List of Figures ix
List of Tables xi
Preface to the Second Edition xii
Preface xx
Modeling Negotiations xx
Overview and Level xxii
Acknowledgments xxv
1. Negotiations in the Bible 1
1.1. Introduction 1
1.2. Cain and Abel: Bargaining with God 3
1.3. Rahab and the Spies: Making a Just Agreement 9
1.4. Solomon’s Arbitration: Discovering the Truth 17
1.5. Conclusions 25
Notes 26
2. Bargaining Procedures and the Problem of Honesty 29
2.1. Introduction 29
2.2. The Honesty Problem 33
2.3. The Bonus Procedure 39
2.4. The Bonus Appraisal Procedure 44
2.5. The Penalty Procedure 47
2.6. The Penalty Appraisal Procedure 50
2.7. The Expansive Appraisal Procedure 52
2.8. Camp David: The Logic of the Procedures Applied 56
2.9. Conclusions 59
Notes 61
3. Arbitration Procedures and the Problem of Convergence 63
vi
3.1. Introduction 63
3.2. Different Arbitration Procedures 65
3.3. Trade-Offs and Implicit Arbitration 67
3.4. Final-Offer Arbitration (FOA) 70
3.5. FOA in Practice: The Importance of Winning 74
3.6. Bonus FOA 78
3.7. Combined Arbitration 80
3.8. Two-Stage and Multistage FOA 84
3.9. Is Convergence in Stages Desirable? 90
3.10. Kissinger’s Shuttle Diplomacy: A Case of Multistage 92
Negotiations
3.11. Conclusions 95
Notes 98
4. Superpower Crisis Bargaining and the Theory of Moves 101
4.1. Introduction 101
4.2. Prisoners’ Dilemma and Chicken 102
4.3. The Cuban Missile Crisis as a Game of Chicken 104
4.4. Deception and Power in the Cuban Missile Crisis 110
4.5. A Sequential View of the Cuban Missile Crisis 113
4.6. The 1973 Alert Decision 116
4.7. Nonmyopic Equilibria and the Theory of Moves: A 120
Digression
4.8. Stability in the Cease-Fire Game 126
4.9. Was There an Alternative to the Alert? 130
4.10. The Possible Effects of Power in the Cease-Fire Game 132
4.11. Conclusions 134
Notes 135
5. Threats and Reputation in Bargaining 139
5.1. Introduction 139
5.2. Repeated Play of a Sequential Game 142
5.3. Threat Outcomes in Repeated Play of a Game 149
5.4. The Sequential-Primary Game 155
5.5. Conclusions 163
vii
Notes 166
6. Threats in Two Domestic Crises 169
6.1. Introduction 169
6.2. The Use of Threat Power in Poland, 1980–81 170
6.3. The White House Tapes Case: The Players and Their 176
Preferences
6.4. The White House Tapes Case: The Trap 182
6.5. Conclusions 187
Notes 188
7. Bargaining in Legislatures 191
7.1. Introduction 191
7.2. Judgments about Vote Trading 193
7.3. Definitions and Assumptions about Vote Trading 194
7.4. Sincere and Insincere Voting 197
7.5. Initial Trades and the Paradox of Vote Trading 201
7.6. Subsequent Trades and the Instability of Vote Trading 204
7.7. The Consequences of Refusing to Trade 206
7.8. The Consequences of Forming Coalitions 208
7.9. Empirical Examples of the Paradox of Vote Trading 211
7.10. Choosing a Governing Coalition in a Multiparty System: 213
Coalition Voting
7.11. Majority, Minimal Majority, and Governing Coalitions 217
7.12. Measuring Bargaining Strength under Coalition Voting 219
7.13. Possible Uses of Coalition Voting 223
7.14. Conclusions 225
Notes 227
8. Bargaining Power 229
8.1. Introduction 229
8.2. Power in the U.S. Federal System 230
8.3. What Should a Power Index Measure? 233
8.4. The Power of Approval and Disapproval 238
8.5. Empirical Evidence of Presidential Power 244
8.6. The Paradox of the Chair’s Position 246
viii
8.7. The Chair’s Counterstrategy of Deception 250
8.8. The Geneva Conference Game 254
8.9. Conclusions 259
Notes 262
9. Epilogue 265
Glossary 269
Bibliography 277
Index 291
Figures
1.1. Game Tree of Cain’s Murder of Abel 8
1.2. Outcome Matrix of Rahab’s Game 11
1.3. Rahab’s Game Revised 13
1.4. Region in Which E(K)>E(B) 17
1.5. Outcome Matrix of Solomon’s Game 19
1.6. Game Tree of Solomon’s Game 21
1.7. Payoff Matrix of Solomon’s Game 21
2.1. Linear Symmetric Equilibrium Strategies of B and S under 35
Chatterjee-Samuelson Procedure
2.2. Discrete Bargaining under the Bonus Procedure 42
2.3. Settlement Regions for Penalty Appraisal Procedure and 53
Expansive Appraisal Procedure: B’s View
3.1. Final Offers of A (a) and B (b) for Uniform Distribution 72
3.2. Gap with and without the Bonus under FOA 78
3.3. Use of Conventional Arbitration and FOA under Combined 81
Arbitration
3.4. Final Offers of A (a) and B (b) for Triangular Distribution 83
4.1. Prisoners’ Dilemma and Chicken 103
4.2. Cuban Missile Crisis as a Game of Chicken 105
4.3. Payoff Matrix of Alternative Representation of the Cuban 107
Missile Crisis
4.4. Game Tree and Payoff Matrix of Sequential Choices in the 114
Cuban Missile Crisis
4.5. Payoff Matrix of Cease-Fire Game 118
4.6. Game Tree of Moves, Starting with Row, from (3,3) in Chicken 123
4.7. Revised Chicken, with Final Outcomes 125
4.8. 1973 Cease-Fire Game (with Alert) as Prisoners’ Dilemma 128
4.9. Cease-Fire Game, with United States as Honest Broker 130
5.1. Moves in Chicken and Prisoners’ Dilemma 143
5.2. Ordinal 2×2 Outcome Matrix 143
5.3. Game Illustrating a Deterrent Threat of Row 147
5.4. Category 1 Games in Which Neither Player Has a Threat 150
Strategy
5.5. Category 2 Games in Which One Player Has a Threat Strategy 151
5.6. Five Category 3 Games in Which Both Players Have a Threat 151
Strategy and Power Is Ineffective