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The formal theory of bargaining originated with John Nash's work in the early 1950s. This book discusses two recent developments in this theory. The first uses the tool of extensive games to construct theories of bargaining in which time is modeled explicitly. The second applies the theory of bargaining to the study of decentralized markets.Rather than surveying the field, the authors present a select number of models, each of which illustrates a key point. In addition, they give detailed proofs throughout the book. n Uses a small number of models, rather than a survey of the field, to illustrate key points n Detailed proofs are given as explanations for the models n Text has been class-tested in a semester-long graduate course
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Reprinted from “Bargaining and Markets”, ISBN 0-12-528632-5, Copyright 1990, with permission from Elsevier. References updated and errors corrected. Version: 2005-3-2.
Bargaining and Markets
This is a volume in ECONOMIC THEORY, ECONOMETRICS, AND MATHEMATICAL ECONOMICS A series of Monographs and Textbooks Consulting Editor: Karl Shell, Cornell University A list of recent titles in this series appears at the end of this volume.
Bargaining and Markets Martin J. Osborne Department of Economics McMaster University Hamilton, Ontario Canada http://www.economics.utoronto.ca/osborne
Ariel Rubinstein Department of Economics Tel Aviv University Tel Aviv, Israel http://arielrubinstein.tau.ac.il
ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers
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This book is printed on acid-free paper. c 1990 by Academic Press, Inc. Copyright All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
Academic Press, Inc. San Diego, California 92101
United Kingdom Edition published by Academic Press Limited 24–28 Oval Road, London NW1 7DX
Library of Congress Cataloging-in-Publication Data Osborne, Martin J. Bargaining and Markets / Martin J. Osborne and Ariel Rubinstein p. cm. Includes bibliographical references. ISBN 0-12-528631-7 (alk. paper). – ISBN 0-12-528632-5 (pbk.: alk. paper) 1. Game Theory. 2. Negotiation. 3. Capitalism. I. Rubinstein, Ariel. II. Title. HB144.073 1990 380.1–dc20 90-30644 CIP
Printed in the United States of America 90 91 92 93 9 8 7 6 5 4 3 2 1
Contents
Preface 1.
Introduction 1.1 Some Basic Terms 1.2 Outline of the Book Notes
Part 1. 2.
ix
The 2.1 2.2 2.3 2.4 2.5 2.6
1 1 3 6
Bargaining Theory Axiomatic Approach: Nash’s Solution Bargaining Problems Nash’s Axioms Nash’s Theorem Applications Is Any Axiom Superfluous? Extensions of the Theory Notes v
7 9 9 11 13 17 20 23 26
vi
Contents
3.
The 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13
4.
The Relation between the Axiomatic and Strategic Approaches 4.1 Introduction 4.2 A Model of Alternating Offers with a Risk of Breakdown 4.3 A Model of Simultaneous Offers: Nash’s “Demand Game” 4.4 Time Preference 4.5 A Model with Both Time Preference and Risk of Breakdown 4.6 A Guide to Applications Notes
5.
Strategic Approach: A Model of Alternating Offers 29 The Strategic Approach 29 The Structure of Bargaining 30 Preferences 32 Strategies 37 Strategies as Automata 39 Nash Equilibrium 41 Subgame Perfect Equilibrium 43 The Main Result 44 Examples 49 Properties of the Subgame Perfect Equilibrium 50 Finite versus Infinite Horizons 54 Models in Which Players Have Outside Options 54 A Gam