Finite allocation mechanisms: approximate Walrasian versus approximate Direct Revelation |
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Authors: | Leonid Hurwicz Thomas Marschak |
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Institution: | (1) Department of Economics, University of Minnesota, Minneapolis, MN 55455, USA (e-mail: hurwicz@tc.umn.edu) , US;(2) Walter A. Haas School of Business, University of California, Berkeley, CA 94720, USA (e-mail: marschak@socrates.berkeley.edu) , US |
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Abstract: | Summary. This paper obtains finite counterparts of previous results that showed the informational efficiency of the Walrasian mechanism
among all mechanisms yielding Pareto-optimal individually rational trades in exchange economies while using a continuum of
possible messages. In particular, we develop finite counterparts of the superiority, with respect to message-space dimension,
of the Walrasian mechanism over Direct Revelation (DR). We measure a finite mechanism's cost by the number of its (equilibrium) messages.
Our two main results are as follows: (1) For exchange economies we find that the overall (maximum) error of a (sufficiently
fine) approximate Walrasian mechanism is less than the overall error of a not-more-costly approximate DR mechanism whose equilibrium
outcomes are trades that are (approximately) Pareto optimal and individually rational; more generally, approximate Walrasian
mechanisms are superior, in the same sense, to approximations of any continuum mechanism whose outcomes are Pareto optimal
individ ually rational trades and whose message space has higher dimension than that of the Walrasian mechanism. (2) As we
increase without limit the dimension of the set of environments (characteristics) defining our class of exchange economies,
the extra cost of DR approximations relative to Walrasian approximations, when both achieve the same overall error, also grows
without limit.
Thus the informational superiority of the Walrasian mechanism emerges again when we approximate it and take the finite number
of messages in the approximation as our cost measure.
Received: June 16, 2002; revised version: July 22, 2002
RID="*"
ID="*" The second author is grateful for support from National Science Foundation grant #IIS-0118600.
Correspondence to: T. Marschak |
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Keywords: | and Phrases: Mechanisms Mechanism design Approximating smooth mechanisms Information processing Exchange economies |
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