Reprinted from “Bargaining and Markets”, ISBN 0-12-528632-5, Copyright 1990, with permission from Elsevier. References updated and errors corrected. Bargaining and Markets Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net 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. Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net Bargaining and Markets Martin J.
Osborne Department of Economics McMaster University Hamilton, Ontario Canada http://www.ca/osborne Ariel Rubinstein Department of Economics Tel Aviv University Tel Aviv, Israel http://arielrubinstein.il ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers San Diego New York Boston London Sydney Tokyo Toronto Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net This book is printed on acid-free paper. Copyright c 1990 by Academic Press, Inc. 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. Includes bibliographical references.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 Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net Contents Preface ix 1.1 Some Basic Terms 1 1.2 Outline of the Book 3 Notes 6 Part 1. The Axiomatic Approach: Nash’s Solution 9 2.5 Is Any Axiom Superfluous? 20 2.6 Extensions of the Theory 23 Notes 26 v Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net vi Contents 3. The Strategic Approach: A Model of Alternating Offers 29 3.1 The Strategic Approach 29 3.2 The Structure of Bargaining 30 3.5 Strategies as Automata 39 3.7 Subgame Perfect Equilibrium 43 3.8 The Main Result 44 3.10 Properties of the Subgame Perfect Equilibrium 50 3.11 Finite versus Infinite Horizons 54 3.12 Models in Which Players Have Outside Options 54 3.13 A Game of Alternating Offers with Three Bargainers 63 Notes 65 4.
The Relation between the Axiomatic and Strategic Approaches 69 4.2 A Model of Alternating Offers with a Risk of Breakdown 71 4.3 A Model of Simultaneous Offers: Nash’s “Demand Game” 76 4.5 A Model with Both Time Preference and Risk of Breakdown 86 4.6 A Guide to Applications 88 Notes 89 5. A Strategic Model of Bargaining between Incompletely Informed Players 91 5.2 A Bargaining Game of Alternating Offers 92 5.4 Delay in Reaching Agreement 104 5.5 A Refinement of Sequential Equilibrium 107 5.6 Mechanism Design 113 Notes 118 Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net Contents vii Part 2. Models of Decentralized Trade 121 6. A First Approach Using the Nash Solution 123 6.2 Two Basic Models 124 6.3 Analysis of Model A (A Market in Steady State) 126 6.4 Analysis of Model B (Simultaneous Entry of All Sellers and Buyers) 128 6.5 A Limitation of Modeling Markets Using the Nash Solution 130 6.7 A Comparison of the Competitive Equilibrium with the Market Equilibria in Models A and B 134 Notes 136 7.
Strategic Bargaining in a Steady State Market 137 7.4 Analysis of Market Equilibrium 143 7.5 Market Equilibrium and Competitive Equilibrium 146 Notes 147 8. Strategic Bargaining in a Market with One-Time Entry 151 8.2 A Market in Which There Is a Single Indivisible Good 152 8.4 A Market in Which There Are Many Divisible Goods 156 8.6 Characterization of Market Equilibrium 162 8.7 Existence of a Market Equilibrium 168 8.8 Market Equilibrium and Competitive Equilibrium 170 Notes 170 9. The Role of the Trading Procedure 173 9.3 A Model of Public Price Announcements 180 9.4 Models with Choice of Partner 182 9.5 A Model with More General Contracts and Resale 185 Notes 187 Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net viii Contents 10. The Role of Anonymity 189 10.4 The No-Discount Assumption 195 10.5 Market Equilibrium and Competitive Equilibrium 197 Notes 197 References 199 Index 211 Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net Preface The formal theory of bargaining originated with John Nash’s work in the early 1950s.
In this book we discuss two recent developments in this theory. The first uses the tool of extensive games to construct theories of bargain- ing in which time is modeled explicitly. The second applies the theory of bargaining to the study of decentralized markets. We do not attempt to survey the field.
Rather, we select a small number of models, each of which illustrates a key point. We take the approach that a thorough analysis of a few models is more rewarding than short discussions of many models. Some of our selections are arbitrary and could be replaced by other models that illustrate similar points. The last section of each chapter is entitled “Notes”.
It usually begins by acknowledging the work on which the chapter is based. (In general we do not make acknowledgments in the text itself.) It goes on to give a brief guide to some of the related work. We should stress that this guide is not complete. We include mainly references to papers that use the model of bargaining on which most of the book is based (the bargaining game of alternating offers).
Almost always we give detailed proofs. Although this makes some of the chapters look “technical” we believe that only on understanding the proofs ix Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net x Preface is it possible to appreciate the models fully. Further, the proofs provide principles that you may find useful when constructing related models. We use the tools of game theory throughout.
Although we explain the concepts we use as we proceed, it will be useful to be familiar with the approach and basic notions of noncooperative game theory. Luce and Raiffa (1957) is a brilliant introduction to the subject. Two other re- cent books that present the basic ideas of noncooperative game theory are van Damme (1987) and Kreps (1990). We have used drafts of this book for a semester-long graduate course.
However, in our experience one cannot cover all the material within the time limit of such a course. A Note on Terminology To avoid confusion, we emphasize that we use the terms “increasing” and “nondecreasing” in the following ways. A function f : R → R for which f (x) > f (y) whenever x > y is increasing; if the first inequality is weak, the function is nondecreasing. A Note on the Use of “He” and “She” Unfortunately, the English language forces us to refer to individuals as “he” or “she”.
We disagree on how to handle this problem. Ariel Rubinstein argues that we should use a “neutral” pronoun, and agrees to the use of “he”, with the understanding that this refers to both men and women. Given our socio-political environment, continuous re- minders of the she/he issue simply divert the reader’s attention from the main issues. Language is extremely important in shaping our thinking, but in academic material it is not useful to wave it as a flag.
Martin Osborne argues that no language is “neutral”. Every choice the author makes affects the reader. “He” is exclusive, and reinforces sexist attitudes, no matter how well intentioned the user. Language has a pow- erful impact on readers’ perceptions and understanding.
An author should adopt the style that is likely to have the most desirable impact on her readers’ views (“the point. is to change the world”). At present, the use of “she” for all individuals, or at least for generic individuals, would seem best to accomplish this goal. We had to reach a compromise.
When referring to specific individuals, we sometimes use “he” and sometimes “she”. For example, in two-player games we treat Player 1 as female and Player 2 as male; in markets games we treat all sellers as female and all buyers as male. We use “he” for generic individuals. Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net Preface xi Acknowledgments The detailed comments of Ken Binmore, Jeroen Swinkels, and Eric van Damme on a draft of the book guided us to significantly improve the accu- racy of the arguments and quality of the exposition.
We are most grateful to them. We are grateful also to Haruo Imai, Jack Leach, Avner Shaked, Asher Wolinsky, John Wooders, and Junsen Zhang for providing valuable comments on several chapters. Ariel Rubinstein’s long and fruitful collaboration with Asher Wolinsky was the origin of many of the ideas in this book, especially those in Part 2. Asher deserves not only our gratitude but also the credit for those ideas.
Martin Osborne gratefully acknowledges support from the Social Sciences and Humanities Research Council of Canada and the Natural Sciences and Engineering Research Council of Canada, and thanks the Kyoto Institute of Economic Research, the Indian Statistical Institute, and the London School of Economics for their generous hospitality on visits during which he worked on this project. Ariel Rubinstein is grateful to the London School of Economics, which was his academic home during the period in which he worked on the book. Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net CHAPTER 1 Introduction 1.1 Some Basic Terms In this book we study sequential game-theoretic models of bargaining and we use them to address questions in economic theory.1 Bargaining Following Nash we use the term “bargaining” to refer to a situation in which (i ) individuals (“players”) have the possibility of concluding a mu- tually beneficial agreement, (ii ) there is a conflict of interests about which agreement to conclude, and (iii ) no agreement may be imposed on any individual without his approval. A bargaining theory is an exploration of the relation between the outcome of bargaining and the characteristics of the situation.
We are not concerned with questions like “what is a just agreement?”, “what is a reasonable outcome for an arbitrator to decide?” or “what agreement is optimal for the society at large?” Nor do we discuss the practical issue of how to bargain effectively. 1 Trắc nghiệm kiến thức chứng khoán Mỹ tại : www. Introduction All the theories that we discuss assume that the individuals are rational, and the theories abstract from any differences in bargaining skill between individuals. We consider (in Chapter 5) the possibility that the individu- als are not perfectly informed, but we maintain throughout the assumption that each individual has well-defined preferences over all relevant outcomes, and, when he has to choose between several alternatives, chooses the alter- native that yields a most preferred outcome.2 Game-Theoretic Models Our main tool is game theory.
We usually describe bargaining situations as (extensive) games. Predictions about the resolution of conflict are derived from game-theoretic solutions (variants of subgame perfect equilibrium). The analysis is intended to be precise. We do not hold the position that every claim in economic theory must be stated formally.
Sometimes formal models are redundant—the arguments can be better made verbally. How- ever, the models in this book, we believe, demonstrate the usefulness of formal models. They provide clear analyses of complex situations and lead us to a better understanding of some economic phenomena. An interpretation of the theories in this book requires an interpretation of game theory.
At several points we make comments on the interpretation of some of the notions we use, but we do not pretend to present a complete and coherent interpretation.3 Sequentiality Almost all the models in this book have a sequential structure: the play- ers have to make decisions sequentially in a pre-specified order.