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Implementation of the Walrasian Correspondence: The Boundary Problem

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Bochet,Olivier (METEOR)

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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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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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Keywords: microeconomics ;

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  1. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Blackwell Publishing, vol. 56(4), pages 603-11, October. [Downloadable!] (restricted)
  2. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September. [Downloadable!] (restricted)
  3. Kunimoto, Takashi & Serrano, Roberto, 2004. "Bargaining and competition revisited," Journal of Economic Theory, Elsevier, vol. 115(1), pages 78-88, March. [Downloadable!] (restricted)
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  4. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-93, November. [Downloadable!] (restricted)
  5. Yildiz, Muhamet, 2003. "Walrasian bargaining," Games and Economic Behavior, Elsevier, vol. 45(2), pages 465-487, November. [Downloadable!] (restricted)
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  6. Bhaskar Dutta & Arunava Sen & Rajiv Vohra, 1994. "Nash implementation through elementary mechanisms in economic environments," Review of Economic Design, Springer, vol. 1(1), pages 173-203, December. [Downloadable!] (restricted)
  7. Gale, Douglas M, 1986. "Bargaining and Competition Part II: Existence," Econometrica, Econometric Society, vol. 54(4), pages 807-18, July. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Blackwell Publishing, vol. 66(1), pages 23-38, January. [Downloadable!] (restricted)
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  10. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer, vol. 4(1), pages 13-33. [Downloadable!] (restricted)
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  11. GIRAUD, Ga‘l & ROCHON, CŽline, 2001. "Consistent collusion-proofness and correlation in exchange economies," CORE Discussion Papers 2001018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  12. Hurwicz, L, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Blackwell Publishing, vol. 46(2), pages 217-25, April. [Downloadable!] (restricted)
  13. Roberto Serrano & Rajiv Vohra, 1997. "Non-cooperative implementation of the core," Social Choice and Welfare, Springer, vol. 14(4), pages 513-525. [Downloadable!] (restricted)
  14. Thomson, W., 1993. ""Divide and Permute" And the Implementation of Solutions to the Problem of Fair Division," RCER Working Papers 360, University of Rochester - Center for Economic Research (RCER).
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
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  2. Olivier, BOCHET & Franois, MANIQUET, 2006. "Virtual Nash implementation with admissible support," Discussion Papers (ECON - Département des Sciences Economiques) 2006043, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
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