STUDIES IN ECONOMIC DESIGN Series Editor Murat R. Sertel Turkish Academy of Sciences Springer Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Tokyo Titles in the Series V. I. Danilov and A. 1. Sotskov Social Choice Mechanisms VI, 191 pages. 2002. ISBN 3-540-43105-5 B. Dutta and M. o. Jackson (Eds.) Networks and Groups VIII, 496 pages. 2003. ISBN 3-540-43113-6 (in preparation) Tatsuro Ichiishi Thomas Marschak Editors Markets, Games, and Organizations Essays in Honor of Roy Radner With 9 Figures and 28 Tables , Springer Professor Tatsuro Ichiishi The Ohio State University Department of Economics 1945 North High Street Columbus, Ohio 43210-1172, USA Email: [email protected] Professor Thomas Marschak University of California Haas School of Business Berkeley, CA 94720, USA First published in "Review of Economic Design, Volume 6, Issue 2,3,4,2001 ISBN 978-3-642-53465-2 ISBN 978-3-540-24784-5 (eBook) DOI 10.1007/978-3-540-24784-5 Library of Congress Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Markets, Games, and Organizations: Essays in Honor of Roy Radner / Ed.: Tatsuro Ichiishi, Thomas Marschak. - Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Tokyo: Springer, 2002 (Studies in Economic Design) ISBN 978-3-642-53465-2 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science + Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 2003 Softcover reprint of the hardcover 1s t edition 2003 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Erich Kirchner, Heidelberg SPIN 10886149 43/2202-5 4 3 2 1 0 - Printed on acid free paper Table of Contents Introduction ................................................... . On characterizing the probability of survival in a large competitive economy Rabi N. Bhattacharya, Mukul Majumdar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Uniqueness of Arrow-Debreu and Arrow-Radner equilibrium when utilities are additively separable Rose-Anne Dana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29 Entry, productivity, and investment Kenneth 1. Arrow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 49 A model of Russia's ''virtual economy" Richard E. Ericson, Barry W. Ickes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 59 Reaction to price changes and aspiration level adjustments [tzhak Gilboa, David Schmeidler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 89 Bargaining solutions with non-standard objectives Peter B. Linhart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99 Investment and concern for relative position Harold L. Cole, George 1. Mailath, Andrew Postlewaite .................. 115 Coordination of economic activity: An example Stanley Reiter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 137 Transversals, systems of distinct representatives, mechanism design, and matching Leonid Hurwicz, Stanley Reiter ..................................... 163 VI Table of Contents Roy Radner and incentive theory Eric S. Maskin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 179 Sufficient conditions for Nash implementation Steven R. Williams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 193 Majority rule with dollar voting James S. Jordan .................................................. 211 Mediation and the Nash bargaining solution Charles A. Wilson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Public spending and optimal taxes without commitment Jess Benhabib, Aldo Rustichini, Andres Velasco ........................ 239 Are "Anti-Folk Theorems" in repeated games nongeneric? Roger Lagunojf, Akihiko Matsui . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Trust and social efficiencies Robert W. Rosenthal .............................................. 281 Survival and the art of profit maximization Prajit K. Dutta, Rangarajan K. Sundaram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Introduction We are pleased to help celebrate Roy Radner's 75th birthday, by issuing in one volume the papers that originally appeared in his honor in two special issues of Review ofE conomic Design (Vol. 6/2 and 6/3-4, 2001). Through his truly original ideas and lucid writing, Roy has influenced and guided the theory community for decades. Many colleagues and students have found their own work shaped and improved by Roy's wide-ranging curiosity, his encouragement, and his keen insights. In soliciting contributions to the Review of Economic Design Radner issues, we decided to approach his former students at the University of California, Berke ley, his former post-doctoral fellows at Bell Laboratories, and his published co authors. We express our sincere apology to any potential authors who fit these categories and whom we may have unintentionally failed to approach. Our job as editors of the Review of Economic Design Radner issues turned out to be easy, thanks to the enthusiastic response we received from authors and the quality of their submissions. The papers in this volume cover quite diverse areas, ranging over general equilibrium analysis of the market mechanism, economies undergoing transi tion, satisficing behavior, markets with asymmetric information, organizational resource allocation and information processing, incentives and implementation, stable sets and the core, stochastic sequential bargaining games, perfect equilib ria in a macro growth model, repeated games, and evolutionary games. Roy's research interests cover all those topics. He has made seminal contributions to most of them, and indeed to so many areas that we shall not attempt a survey. In what follows, we briefly introduce the seventeen papers. General equilibrium analysis of the market mechanism. The paper by Rabi N. Bhattacharya and Mukul K. Majumdar, "On characterizing the probability of sur vival in a large competitive economy," introduces a survival constraint into the random pure exchange economy, and studies the competitive eqUilibrium price vector (a random variable) and the probability of ruin, as the size of the economy (the number of consumers) becomes infinitely large. It provides a sensitivity anal- 2 Introduction ysis of the survival probability with respect to a change in the limiting averages of the endowments over the agents. The paper by Rose-Anne Dana, "Unique ness of Arrow-Debreu and Arrow-Radner equilibria when utilities are additively separable," surveys various approaches to the unique existence of a competitive equilibrium (called the Arrow-Debreu equilibrium) of a pure exchange economy when consumers' utility functions are additively separable, and to the unique existence of a competitive eqUilibrium (called the Arrow-Radner equilibrium) of a one-commodity two-period pure exchange economy with securities. The author has been one of the key players in this research area, especially for the economy with infinitely many commodities (or with infinitely many states for the economy with securities). Economies undergoing transition. In the paper by Kenneth J. Arrow, "Entry, production, and investment," the author first points out two modes of transition from the government controlled economy to the free market economy, by priva tization and by free entry, and argues that the latter mode is more efficient. The paper concerns the latter mode, and provides policy guidance. The problems are caused by two basic facts: limited financial resources and uncertainty about the productivity of new entrants. The issue here is, therefore, how many entrants are to be financed. The author's first conclusion is that if the same adequate sup port level is given to all the supported entrants, then it is optimal to encourage multiple entry, although that may be constrained by resource availabilities. He then considers differentiated financing strategies; his second conclusion is that there is a gain by including a possibly inadequate level of financing of a firm. Finally, he analyzes the effect of entry on savings for the situation in which the marginal returns of the entrants are initially higher than the market return. In the paper by Richard E. Ericson and Barry W. Ickes, "A model of Russia's 'virtual economy'," the authors first point out that the Russian economy has evolved into the so-called virtual economy, a partially monetized quasi-market system. Here, inefficient enterprises engage in barter. The authors construct a simple partial equilibrium model of the energy market, in which there are an energy-supplying monopolist and a continuum of energy-demanding enterprises with differing degrees of efficiency. The main results of the paper concern an eqUilibrium (a "trap") in which inefficient enterprises decline to restructure, and hence they hinder the transition to a free-market economy. Satisficing behavior. The paper by Itzhak Gilboa and David Schmeidler, "Re action to price changes and aspiration level adjustments," studies examples of a consumer's satisficing behavior, in which his past actions and his observed market prices determine an aspiration level, and his aspiration level in turn de termines his preference relation, and so influences his action. Implications for a comparative statics problem (the study of the consumer's responses to several modes of changes in a price) are explored. In particular, results contradictory to the neoclassical results (which are based on the postulate of consumer's optimiz ing behavior) are obtained. Introduction 3 Markets with asymmetric information. The paper by Peter Linhart, "Bargaining equilibria with non-standard objectives," studies a model of sealed-bid bargain ing of one item with one seller and one buyer. The seller knows the cost of the item, but cannot observe the buyer's action (bid), and there is a symmetric sce nario for the buyer. Two alternative objectives are proposed, and the associated noncooperative equilibria in pure strategies are studied: one objective is mini mization of maximal regret, and the other objective is maximization of maximal profit. Given the former objective, the author's equilibrium is close in spirit to an a-individually rational strategy bundle, and he shows it to be unique in some important special cases. Organizational resource allocation and information processing. The paper by Harold Cole, George J. Mailath and Andrew Postlewaite, "Investment and con cern for relative position," studies the effect of non-market considerations (mar riage) on decision-making in the market (investment), given a continuum of females and a continuum of males: A female first makes an investment decision, and after realization of the return of her investment, she plays a matching game for marriage. A female's first decision influences her position in the marriage game. The paper by Stanley Reiter, "Coordination of economic activity: An ex ample," constructs a formal model to address coordination of managers' decisions either through a market mechanism or through a direct (nonmarket) mechanism, when managers' pursuit of self interest is abstracted away. The author examines two examples. In one example, the market mechanism does not result in efficient coordination, and so it is ruled out. In the other example, both the market and the nonmarket mechanism bring about efficient coordination, so the two mechanisms are compared in order to identify the one that has lower informational cost. The paper by Leonid Hurwicz and Stanley Reiter, "On transversals and systems of distinct representatives," establishes a necessary and sufficient condition for a family \?? of subsets of a set W to have a system of distinct representatives (that is, there exists a 1-1 mapping A : \?? --+ e, e c W, such that A(K) E K for every K E \??). The question of existence of a system of distinct representatives arises in designing decentralized mechanisms to meet a given optimality crite rion, as well as in matching games. The authors also establish several necessary and sufficient conditions for a family ~' to be a partition of the set W. Incentives and Implementation. The paper by Eric S. Maskin, "Roy Radner and incentive theory," provides a self-contained integrate survey of some incentives issues when individuals are endowed with private information. These issues in clude: implementation in dominant strategies in the presence of adverse selection; welfare loss due to moral hazard in a one-principal, one-agent model; its approx imate recovery as a perfect Bayesian equilibrium of the associated repeated game (in which players maximize their discounted sum of payoffs); and welfare loss due to double moral hazard in a partnership model. Brief comments on imple mentation in Nash or Bayesian equilibrium are also given. The original version of the paper by Steve Williams, "Sufficient conditions for Nash implementation," was written in Spring 1984, and had been circulated as a well-known discussion 4 Introduction paper since then. It clarifies some difficulties inherent in Maskin's conjecture on Nash implementation, and settles the matter positively. Given a social choice correspondence F which satisfies monotonicity and no veto power, the paper first presents Maskin's sufficient condition on a game form (S, g) under which (S, g) implements F in Nash eqUilibrium. The paper then quotes the author's own pub lished result establishing a sufficient condition for F to be Nash implementable. Here, Maskin's assumption of finiteness of the outcome space is replaced by a new condition on the cardinality of F-1(a) for each outcome a. The paper points out that given an objective F satisfying these assumptions, Maskin's procedure produces a game form which satisfies Maskin's sufficient condition for Nash implementation of F. The paper also provides an example of an F which sat isfies monotonicity and no veto power, fails to satisfy the author's condition on cardinality of F-1(a), and cannot be implemented by the game form produced by Maskin's procedure. Finally the paper establishes that the author's condition on cardinality of F-1(a) is not needed after all for Nash implementability (if one is not required to use the game form obtained by Maskin's procedure). Stable sets and the core. The paper by James S. Jordan, "Majority rule with dollar voting," considers a society whose total wealth is allocated to its members. Given any allocation, a coalition whose members have been allocated, in total, more than a half of the society's wealth is considered a majority, and is empowered to re-distribute the society's total wealth to its members. Thus, the concept of dominance relative to an allocation is well-defined (although the model cannot be reduced to a game in characteristic function form). Only extreme concentration of wealth, in which one player owns everything or two players each own half of the total wealth are undominated, and thus constitute the core. However, the stable set (the Von Neumann-Morgenstern solution) is significantly larger. Allocations in which one player has half the wealth, or which divide the total wealth equally among a number of players equal to a power of two, constitute the unique stable set. The stable set thus provides a formal model of an endogenous balance of power. Stochastic sequential bargaining games. The paper by Charles A. Wilson, "Me diation and the Nash bargaining solution," studies the following two-person se quential bargaining game with a mediator, and shows that as the discount rates become arbitrarily small, the subgame perfect payoffs converge to the asymmetric Nash bargaining solution, with weights determined by the relative discount rates of the players. The mediator announces a payoff allocation to the two players according to an exogenously given density function f (hence a proposed payoff allocation is not an endogenous variable in the game), and then the two players sequentially choose either to accept it or reject it. If both players accept it, then the game is over. If one player rejects it, another round of the game is played, in which the mediator proposes a payoff allocation according to the same function f· Perfect equilibria in a macro growth model. The paper by Jess Benhabib, Aldo Rustichini and Andres Velasco, "Public spending and optimal taxes without com-