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Implementation of the Walrasian correspondence: the boundary problem

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  • BOCHET, Olivier

Abstract

Consider exchange economies in which preferences are continuous, convex and strongly monotonic. It is well known that the Walrasian correspondence is not Nash implementable. Maskin monotonicity (Maskin, 1999) is violated for allocations at the boundary of the feasible set. We derive an impossibility result showing that it is in fact not implementable in any solution concept. Next, we construct a sequential mechanism based on price-allocation announcements that fits the very description of Walrasian Equilibrium. Imposing an additional domain restriction, we show that it fully implements the Walrasian correspondence in subgame perfect and strong subgame perfect equilibrium. We thus take care of the boundary problem that was prominent in the Nash implementation literature.

Suggested Citation

  • BOCHET, Olivier, 2005. "Implementation of the Walrasian correspondence: the boundary problem," CORE Discussion Papers 2005060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2005060
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    Cited by:

    1. Bochet, Olivier & Maniquet, François, 2010. "Virtual Nash implementation with admissible support," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 99-108, January.
    2. Michele Lombardi & Naoki Yoshihara, 2017. "Natural implementation with semi-responsible agents in pure exchange economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1015-1036, November.
    3. Bochet, Olivier, 2006. "Equal-Budget Choice Equivalent Solutions in Exchange Economies," Research Memorandum 025, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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