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Implementation of the Walrasian Correspondence: The Boundary Problem

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  • Bochet,Olivier

    (METEOR)

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-allocationannouncements 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.

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Bibliographic Info

Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 037.

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Date of creation: 2005
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Handle: RePEc:dgr:umamet:2005037

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Web page: http://www.maastrichtuniversity.nl/web/UMPublications.htm

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Keywords: microeconomics ;

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  3. repec:fth:louvco:01-18 is not listed on IDEAS
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  9. Gale, Douglas M, 1986. "Bargaining and Competition Part II: Existence," Econometrica, Econometric Society, vol. 54(4), pages 807-18, July.
  10. William Thomson, 2004. "Divide-and-Permute," RCER Working Papers 510, University of Rochester - Center for Economic Research (RCER).
  11. Thomson, W., 1996. "Monotonic Extension on Economic Domains," RCER Working Papers 431, University of Rochester - Center for Economic Research (RCER).
  12. GIRAUD, Gaël & ROCHON, Céline, 2001. "Consistent collusion-proofness and correlation in exchange economies," CORE Discussion Papers 2001018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. Saijo, Tatsuyoshi, 1988. "Strategy Space Reduction in Maskin's Theorem: Sufficient Conditions for Nash Implementation," Econometrica, Econometric Society, vol. 56(3), pages 693-700, May.
  14. Roberto Serrano & Rajiv Vohra, 1997. "Non-cooperative implementation of the core," Social Choice and Welfare, Springer, vol. 14(4), pages 513-525.
  15. Serrano, Roberto & Vohra, Rajiv, 2002. "Bargaining and Bargaining Sets," Games and Economic Behavior, Elsevier, vol. 39(2), pages 292-308, May.
  16. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 603-11, October.
  17. Guoqiang Tian, 2000. "Feasible and Continuous Double Implementation of Constrained Walrasian Allocations," Annals of Economics and Finance, Society for AEF, vol. 1(1), pages 19-32, May.
  18. Abreu, Dilip & Sen, Arunava, 1990. "Subgame perfect implementation: A necessary and almost sufficient condition," Journal of Economic Theory, Elsevier, vol. 50(2), pages 285-299, April.
  19. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  20. Hurwicz, L, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 217-25, April.
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Cited by:
  1. BOCHET, Olivier & MANIQUET, François, 2006. "Virtual Nash implementation with admissible support," CORE Discussion Papers 2006084, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Veiga, Helena & Vorsatz, Marc, 2006. "Price Manipulation in an Experimental Asset Market," Research Memoranda 024, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.

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