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Implementation of the Walrasian correspondence: the boundary problem

  • BOCHET, Olivier

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.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2005060.

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Date of creation: 00 Sep 2005
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Handle: RePEc:cor:louvco:2005060
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  1. 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.
  2. 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).
  3. Roberto Serrano & Rajiv Vohra, 1997. "Non-cooperative implementation of the core," Social Choice and Welfare, Springer, vol. 14(4), pages 513-525.
  4. Takashi Kunimoto & Roberto Serrano, 2002. "Bargaining and Competition Revisited," Working Papers 2002-14, Brown University, Department of Economics.
  5. Muhamet Yildiz, 2002. "Walrasian Bargaining," Theory workshop papers 505798000000000003, UCLA Department of Economics.
  6. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 603-11, October.
  7. 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.
  8. Thomson, W., 1996. "Monotonic Extension on Economic Domains," RCER Working Papers 431, University of Rochester - Center for Economic Research (RCER).
  9. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-93, November.
  10. 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.
  11. 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.
  12. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  13. Gale, Douglas M, 1986. "Bargaining and Competition Part II: Existence," Econometrica, Econometric Society, vol. 54(4), pages 807-18, July.
  14. William Thomson, 2004. "Divide-and-Permute," RCER Working Papers 510, University of Rochester - Center for Economic Research (RCER).
  15. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
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