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Finite allocation mechanisms: approximate Walrasian versus approximate Direct Revelation


  • Leonid Hurwicz
  • Thomas Marschak


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. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Leonid Hurwicz & Thomas Marschak, 2003. "Finite allocation mechanisms: approximate Walrasian versus approximate Direct Revelation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 545-572, March.
  • Handle: RePEc:spr:joecth:v:21:y:2003:i:2:p:545-572
    DOI: 10.1007/s00199-002-0320-9

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    Cited by:

    1. Marschak, Thomas, 2006. "Organization Structure," MPRA Paper 81518, University Library of Munich, Germany.
    2. Nisan, Noam & Segal, Ilya, 2006. "The communication requirements of efficient allocations and supporting prices," Journal of Economic Theory, Elsevier, vol. 129(1), pages 192-224, July.

    More about this item


    Keywords and Phrases: Mechanisms; Mechanism design; Approximating smooth mechanisms; Information processing; Exchange economies.; JEL Classification Numbers: D20; D50; D80; D83.;

    JEL classification:

    • D20 - Microeconomics - - Production and Organizations - - - General
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General


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