Communication in Economic Mechanisms

This chapter considers the problem of …nding allocations that satisfy certain social goals when economic agents have private information about their preferences. While economists have traditionally considered the problem of providing incentives for agents to fully reveal their preferences, such full revelation is often impractical or undesirable, for several reasons: (1) it may require a prohibitive amount of communication as measured in bits or real numbers, (2) it may be costly for agents to evaluate their complete preferences, and (3) the revealed information may be exploited by the designer or other agents. Thus, we consider the question: What is the minimal information that must be elicited from the agents in order to achieve the goals? Note that the question arises even if agents can be counted on to report truthfully. Segal (2005) shows that for a large class of social problems, any minimally informative way to verify that a given alternative is desirable is equivalent to giving each agent This chapter was prepared for the 9th World Congress of the Econometric Society, London, August 19-24, 2005. I gratefully acknowledge …nancial support of the National Science Foundation (grants SES 0214500, 0427770). I also thank my discussant, Roger Myerson, and the participants of too many seminars and conference presentations where some of the research surveyed in the chapter was presented. In particular, I am grateful to Susan Athey, Jonathan Levin, Eric Maskin, Paul Milgrom, Andy Postlewaite, Thomas Sjostrom, and James Jordan for discussions related to this topic. Last but not least, I am indebted to my coauthors Noam Nisan and Ronald Fadel for helping clarify my understanding of the topics discussed in this chapter. yDepartment of Economics, Stanford University, Stanford, CA 94305. Email: ilya.segal@stanford.edu

[1]  Xavier Calsamiglia,et al.  Decentralized resource allocation and increasing returns , 1977 .

[2]  Peter J. Hammond,et al.  Game Forms versus Social Choice Rules as Models of Rights , 1996 .

[3]  Werner Hildenbrand,et al.  Mathematical Economics: Valuation equilibrium and Pareto optimum , 1983 .

[4]  Dilip Mookherjee,et al.  A theory of responsibility centers , 1992 .

[5]  Wouter Dessein Authority and Communication in Organizations , 2002 .

[6]  Theodore Groves,et al.  Information, Incentives, and Economic Mechanisms: Essays in Honor of Leonid Hurwicz , 1987 .

[7]  Yuval Rabani,et al.  Linear Programming , 2007, Handbook of Approximation Algorithms and Metaheuristics.

[8]  Harold Abelson,et al.  Lower bounds on information transfer in distributed computations , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[9]  John N. Tsitsiklis,et al.  Communication complexity of algebraic computation , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[10]  V. Crawford,et al.  Job Matching, Coalition Formation, and Gross Substitutes , 1982 .

[11]  Stan Lipovetsky,et al.  Designing Economic Mechanisms , 2007, Technometrics.

[12]  H. Simon,et al.  A Formal Theory of the Employment Relationship , 1951 .

[13]  F. Ygge Optimal Auction Design for Agents with Hard Valuation Problems , .

[14]  S. Reichelstein Incentive compatibility and informational requirements , 1984 .

[15]  S. Reiter,et al.  The informational size of message spaces , 1974 .

[16]  A. Sen,et al.  The Impossibility of a Paretian Liberal , 1970, Journal of Political Economy.

[17]  Alvin E. Roth,et al.  Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis , 1990 .

[18]  Thomas Marschak,et al.  Mechanisms that efficiently verify the optimality of a proposed action , 1996 .

[19]  Thomas Marschak,et al.  Finite allocation mechanisms: approximate Walrasian versus approximate Direct Revelation , 2003 .

[20]  Fumitaka Sato,et al.  On the informational size of message spaces for resource allocation processes in economies with public goods , 1981 .

[21]  S. Landsburg The Armchair Economist: Economics and Everyday Life , 1993 .

[22]  Thomas Marschak,et al.  Network Mechanisms, Informational Efficiency, and Hierarchies , 1998 .

[23]  Felix Brandt,et al.  Unconditional privacy in social choice , 2005, TARK.

[24]  Paul R. Milgrom,et al.  Matching with Contracts , 2005 .

[25]  Andreu Mas-Colell,et al.  Efficiency and Decentralization in the Pure Theory of Public Goods , 1980 .

[26]  Oscar Volij,et al.  Walrasian Allocations without Price-Taking Behavior , 2000, J. Econ. Theory.

[27]  Vincent Conitzer,et al.  Communication complexity of common voting rules , 2005, EC '05.

[28]  G. A. Edgar Measure, Topology, and Fractal Geometry , 1990 .

[29]  Noam Nisan,et al.  Approximation algorithms for combinatorial auctions with complement-free bidders , 2005, STOC '05.

[30]  R. Radner Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices , 1979 .

[31]  N. Nisan,et al.  Exponential Communication Ine ¢ ciency of Demand Queries , 2004 .

[32]  Biung-Ghi Ju,et al.  Nash Implementation and Opportunity Equilibrium , 2005 .

[33]  Robert W. Irving,et al.  The Stable marriage problem - structure and algorithms , 1989, Foundations of computing series.

[34]  Sanford J. Grossman An Introduction to the Theory of Rational Expectations Under Asymmetric Information , 1981 .

[35]  Joan Feigenbaum,et al.  Computation in a distributed information market , 2003, EC '03.

[36]  E. Maskin Nash Equilibrium and Welfare Optimality , 1999 .

[37]  S. Reiter,et al.  Game forms with minimal message spaces , 1988 .

[38]  D. MacKenzie,et al.  The use of knowledge about society , 2008 .

[39]  Dilip Mookherjee Decentralization, Hierarchies, and Incentives: A Mechanism Design Perspective , 2006 .

[40]  S. Bikhchandani,et al.  Competitive Equilibrium in an Exchange Economy with Indivisibilities , 1997 .

[41]  A. Mas-Colell,et al.  Microeconomic Theory , 1995 .

[42]  Xavier Calsamiglia,et al.  Informational Requirements of Parametric Resource Allocation Processes , 1981 .

[43]  J. Tirole,et al.  Formal and Real Authority in Organizations , 1997, Journal of Political Economy.

[44]  Joan Feigenbaum,et al.  Hardness Results for Multicast Cost Sharing , 2002, FSTTCS.

[45]  Gerard Debreu,et al.  A Social Equilibrium Existence Theorem* , 1952, Proceedings of the National Academy of Sciences.

[46]  J. Jordan The competitive allocation process is informationally efficient uniquely , 1982 .

[47]  Eiichi Miyagawa,et al.  Reduced-Form Implementation , 2002 .

[48]  Bernard Salanié,et al.  The Economics of Contracts: A Primer , 1997 .

[49]  F. Hayek The economic nature of the firm: The use of knowledge in society , 1945 .

[50]  Elchanan Mossel,et al.  On approximately fair allocations of indivisible goods , 2004, EC '04.

[51]  Moshe Babaioff,et al.  Computationally-feasible truthful auctions for convex bundles , 2008, Games Econ. Behav..

[52]  David C. Parkes,et al.  Price-Based Information Certificates for Minimal-Revelation Combinatorial Auctions , 2002, AMEC.

[53]  Steven R. Williams Realization and Nash Implementation: Two Aspects of Mechanism Design , 1986 .

[54]  Joan V. Robinson,et al.  The Nature of the Firm , 2004 .

[55]  Sushil Bikhchandani,et al.  The Package Assignment Model , 2002, J. Econ. Theory.

[56]  Noam Nisan,et al.  The communication requirements of efficient allocations and supporting prices , 2006, J. Econ. Theory.

[57]  David C. Parkes,et al.  Optimal Auction Design for Agents with Hard Valuation Problems , 1999, Agent Mediated Electronic Commerce.

[58]  AbelsonHarold Lower Bounds on Information Transfer in Distributed Computations , 1980 .

[59]  Joseph Greenberg,et al.  The Theory of Social Situations: An Alternative Game-Theoretic Approach , 1990 .

[60]  Jean-Claude Milleron,et al.  Theory of value with public goods: A survey article☆ , 1972 .

[61]  Joseph E. Stiglitz,et al.  Rational Expectations Equilibrium : Generic Existence and the Information Revealed by Prices , 2007 .

[62]  Federico Echenique Counting combinatorial choice rules , 2007, Games Econ. Behav..