Competition, Collusion, and Game Theory ALDINE TREATISES IN MODERN ECONOMICS edited by Harry G. Johnson University of Chicago and London School Of Economics Competition, Collusion, and Game Theory LESTER G. TELSER University of Chicago P ALGRAVE MACMILLAN ABOUT THE AUTHOR Lester G. Telser, Professor of Economics at the University of Chicago, received his Ph.D. from that university in 1956. One of the world's leading mathematical economists, he has been a Visiting Research Fellow, Cowles Foundation for Research in Economics, Yale University; Faculty Research Fellow, Ford Foundation; and Assistant Professor of Economics, Iowa State University. ISBN 978-1-349-01540-5 ISBN 978-1-349-01538-2 (eBook) DOI 10.1007/978-1-349-01538-2 © Lester G. Telser 1971 Softcover reprint of the hardcover 1St edition 1971 978-0-333-13644-7 All rights reserved. No part of this publication may be reproduced or transmitted, in any form or by any means, without permission. First published in the U.S.A. 1972 by Aldine • Atherton, Inc. First published in the United Kingdom 1972 Published by THE MACMILLAN PRESS LTD London and Basingstoke Associated companies in New York Toronto Dublin Melbourne Johannesburg and Madras SBN 333 13644 6 TO JOSHUA AND TAMAR Foreword For only a little over a decade, economic theorists have been working on a new and fundamental approach to the theory of competition and market structure, an approach inspired by appreciation of the earlier work of Edgeworth and Bohm-Bawerk and making use of the new tools of the theory of games as developed by von Neumann and Morgenstern. This new approach bases itself on the analysis of competitive behavior and its impli­ cations for the characteristics of market equilibrium rather than on assump­ tions about the characteristics of competitive and monopolistic markets. Its central concept is "the theory of the core of the market," and it is concerned, very broadly speaking, with the conditions under which markets will or will not achieve the characteristics of uniform prices and welfare optimality posited by traditional theory. This concern entails, among other things, a shift of emphasis from the prevailing concentration on oligopoly as a type of market structure and on advertising as a weapon of competition to the influence on the outcome of market processes of such factors as number of traders on the two sides of the market, transactions costs, brokerage, the way in which firms form their expectations of future demand, and the costs of collusion. Professor Lester' G. Telser has been at the forefront of the development of the new approach and is one of the few practitioners of it capable of com­ municating to his fellow economists its theoretical techniques and, more important, its implications for the empirical analysis of market phenomena. This he does both by the construction and analysis of simple economic problems to illustrate the theory and by the presentation of empirical research of his own designed to formulate and test propositions suggested by the new "theory of the core" approach to market analysis. His own introduction provides a sufficiently concise summary of the scope of the book to make it vii Vlll Foreword unnecessary for me to attempt a still briefer summary here. Suffice it to say that this is the first book to present a comprehensive synthetic overview of an important new line of development in fundamental economic theory and that I am delighted to be associated with its publication as an Aldine Treatise. HARRY G. JOHNSON Acknowledgments The research presented in this book has received the generous support of the National Science Foundation, initiated with grant GS-365 in 1963 and continued with grant GS-1783 in 1966. This financial aid was indispensable in carrying out the work. It made possible my sojourn as a visiting research fellow at the Cowles Foundation for Research in Economics for the academic year 1964-65 where I first learned about the theory of the core. In 1969-70 I received a Ford Faculty Research Fellowship, which enabled me to finish this book. During this time I worked at the Center for Operations Research and Econometrics at the Catholic University of Louvain, Belgium. Much of the material in this book has been exposed to my students in the course "Theories of Competition," which I have taught in the economics department at the University of Chicago for the past five years. The com­ ments of the students in this course have taught me a great deal; of particular helpfulness were those of Uri Ben-Zion, Y o ram Peles, and Donald Parsons. I have also been fortunate in having the aid of several very able research assistants. E. H. Thornber gave invaluable assistance in carrying out the empirical analysis reported in chapter VII. The work in chapter VIII was done with the assistance of Uri Ben-Zion, Harry Bloch, Josef May, and Stan Horowitz. Carl Berliner helped with appendix 4 of chapter VIII. I am also very grateful to many of my professional colleagues for their comments and criticisms of various parts of the book. In particular, Lloyd Shapley and Herbert Scarf saved me from some serious errors in chapter II when I presented this material at the Mathematical Social Science Board Seminar on Game Theory at the RAND Corporation, Santa Monica, California, in June 1969. The research in chapter VIII has benefited from the comments by H. Gregg Lewis, Walter Oi, George Stigler, and Leonard Weiss. Zvi Griliches has read and commented on both chapters VII and IX x Acknowledgements VIII. Yoram Barzel read with painstaking care chapters I, V, VII, and VIII. Much of the improvement in the exposition was inspired by the comments of Harry Johnson and Robert Wesner. Charles Cox and Howard Marvel eliminated errors in the final stages by reading the proofs and checking the index. I must assume, however, the sole responsibility for any errors and shortcomings in this book and must absolve all of those mentioned from any blame for these. One other person has been a constant source of encouragement as well as a sounding board for my ideas-my wife, Sylvia. The burden of editing and preparing the manuscript for publication, of endless checking, and of polishing the style was lightened thanks to her help. Contents Foreword vii Acknowledgments xi Introduction xiii I. APPLICATIONS OF CORE THEORY TO MARKET EXCHANGE 3 I. Introduction 3 2. Consumer Surplus and Tmnsferable Utility 4 3. Some Simple Tmding Situations 11 4. m Owners and n Nonowners 19 5. The Basic Core Constraints 28 6. Market Efficiency and Honest Brokers 31 7. Multiunit Trade 37 8. Increasing Returns and Public Goods from the Viewpoint of the Core 48 9. A Brief Historical Note 57 Appendix: Consumer Surplus 62 II. FURTHER ApPLICATIONS OF CORE THEORY TO MARKET EXCHANGE 68 1. Introduction 68 2. Balanced Collections of Coalitions 70 3. Empty Cores 78 4. The Feasibility of Trade 88 5. Group Rationality with Multiunit Trade 94 6. Competition and Numbers 104 7. The Number of Traders and the Emptiness of the Core 108 8. Conclusions 117 III. APPLICATIONS OF THE CoRE TO OLIGOPOLY 119 1. Introduction 119 2. Properties of the Core under Constant Returns 124 3. The Cournot-Nash Theory of Duopoly for Finite Horizons 131 4. The Coumot-Nash Theory of Duopoly for Infinite Horizons 142 xii Contents IV. THEORIES OF EXPECTATIONS FOR N CoMPETING FIRMS 146 1. Introduction 146 2. Expectation Models with Quantity as the Policy Variable 149 3. Expectation Models for Price as the Policy Variable 164 4. Summary 172 V. COMPETITION OR COLLUSION? 175 l. Introduction 175 2. The Nature of Competition and Collusion 176 3. Equilibrium with Product Variety Illustrated for Spatial Competition 184 4. The Costs of Maintaining Collusion 192 5. Sharing the Collusive Return 206 VI. THE MONOPOLY AND CoURNOT-NASH EQUILffiRIA UNDER DYNAMIC CoNDITIONS 218 l. Introduction 218 2. Dynamic Demand Relations 221 3. Some Fundamentals on Optimal Policies 226 4. The Solvability of Certain Linear Equations 242 5. Properties of the Cooperative and Noncooperative Dynamic Equilibria 250 6. Conclusions 272 VII. EsTIMATES OF DEMAND, PRICE PoLICY, AND THE RATIO OF PRICE TO MARGINAL CosT BY BRAND FOR SELECTED CoNSUMER GooDS 274 l. Introduction 274 2. Estimates of the Demand Relation between Market Share and Prices 283 3. Estimates of the Relations among Competing Prices 294 4. Competition in a New Product 299 5. Conclusions 305 VIII. SOME DETERMINANTS OF THE RETURNS TO MANUFACTURING INDUSTRIES 312 l. Introduction 312 2. Description of the Data and Some Simple Summary Statistics 316 3. Multiple Regression Analysis of the Census Data 324 4. An Analysis of Employment Turnover in Selected Manufacturing Industries 339 5. A Brief Survey of Findings by Other Investigators 352 6. Conclusions 356 Appendix 1 : Estimation of Payrolls, Annual Earnings, and Employment of Nonproduction Workers 357 Appendix 2: Description of the Samples 359 Appendix 3: The Two-Digit Industry Effects 361 Appendix 4: The Relative Size Distribution of Firms 363 References 367 Name Index 371 Subject Index 372 Introduction Although the nature of a market and what happens there is surely a proper subject of economic analysis, the student will search the literature in vain for more than passing mention of this fundamental topic prior to 1881 when Edgeworth published his profound analysis of markets. The next important contribution did not appear until a decade later in Bohm-Bawerk's cele­ brated study of a horse market containing the first rigorous constructions of market supply and demand schedules. This paucity of early analysis is all the more surprising when we recall that in the 1870s economics embarked on its modem rigorous course with the contributions of Jevons, Menger, and Walras.