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Implementation of the Walrasian correspondence: the boundary problem

  • Olivier Bochet


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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Article provided by Springer & Game Theory Society 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
DOI: 10.1007/s00182-007-0103-4
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  1. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-93, November.
  2. L. Hurwicz, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Oxford University Press, vol. 46(2), pages 217-225.
  3. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
  4. Thomson, W., 1996. "Monotonic Extension on Economic Domains," RCER Working Papers 431, University of Rochester - Center for Economic Research (RCER).
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  6. Kunimoto, Takashi & Serrano, Roberto, 2004. "Bargaining and competition revisited," Journal of Economic Theory, Elsevier, vol. 115(1), pages 78-88, March.
  7. William Thomson, 2004. "Divide-and-Permute," RCER Working Papers 510, University of Rochester - Center for Economic Research (RCER).
  8. 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.
  9. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  10. Yildiz, Muhamet, 2003. "Walrasian bargaining," Games and Economic Behavior, Elsevier, vol. 45(2), pages 465-487, November.
  11. Andrew Postlewaite & David Wettstein, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 603-611.
  12. 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.
  13. Roberto Serrano & Rajiv Vohra, 1997. "Non-cooperative implementation of the core," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(4), pages 513-525.
  14. Bhaskar Dutta & Arunava Sen & Rajiv Vohra, 1994. "Nash implementation through elementary mechanisms in economic environments," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 173-203, December.
  15. 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.
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