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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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File URL: http://hdl.handle.net/10.1007/s00182-007-0103-4
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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. 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.
  2. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
  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. 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.
  5. Gale, Douglas M, 1986. "Bargaining and Competition Part II: Existence," Econometrica, Econometric Society, vol. 54(4), pages 807-18, July.
  6. 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.
  7. 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.
  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. Thomson, William, 2005. "Divide-and-permute," Games and Economic Behavior, Elsevier, vol. 52(1), pages 186-200, July.
  10. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-93, November.
  11. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer;Society for Economic Design, vol. 4(1), pages 13-33.
  12. Takashi Kunimoto & Roberto Serrano, 2002. "Bargaining and Competition Revisited," Working Papers 2002-14, Brown University, Department of Economics.
  13. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  14. Yildiz, Muhamet, 2003. "Walrasian bargaining," Games and Economic Behavior, Elsevier, vol. 45(2), pages 465-487, November.
  15. Andrew Postlewaite & David Wettstein, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 603-611.
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