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Implementation of the Walrasian correspondence: the boundary problem

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  • Olivier Bochet

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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-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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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 36 (2007)
Issue (Month): 2 (October)
Pages: 301-316

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Handle: RePEc:spr:jogath:v:36:y:2007:i:2:p:301-316

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Related research

Keywords: Walrasian equilibrium; Implementability; Justified sensitivity; Double implementation; Subgame perfect equilibrium; Strong subgame perfect equilibrium;

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References

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  1. Thomson, W., 1996. "Monotonic Extension on Economic Domains," RCER Working Papers 431, University of Rochester - Center for Economic Research (RCER).
  2. Roberto Serrano & Rajiv Vohra, 1997. "Non-cooperative implementation of the core," Social Choice and Welfare, Springer, vol. 14(4), pages 513-525.
  3. 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.
  4. Giraud, Gael & Rochon, Celine, 2002. "Consistent collusion-proofness and correlation in exchange economies," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 441-463, December.
  5. Kunimoto, Takashi & Serrano, Roberto, 2004. "Bargaining and competition revisited," Journal of Economic Theory, Elsevier, vol. 115(1), pages 78-88, March.
  6. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 603-11, October.
  7. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  8. Thomson, William, 2005. "Divide-and-permute," Games and Economic Behavior, Elsevier, vol. 52(1), pages 186-200, July.
  9. Muhamet Yildiz, 2002. "Walrasian Bargaining," Theory workshop papers 505798000000000003, UCLA Department of Economics.
  10. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-93, November.
  11. 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.
  12. 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.
  13. Gale, Douglas M, 1986. "Bargaining and Competition Part II: Existence," Econometrica, Econometric Society, vol. 54(4), pages 807-18, July.
  14. repec:fth:louvco:01-18 is not listed on IDEAS
  15. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  16. 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.
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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. 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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