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Virtual Nash implementation with admissible support


  • Bochet, Olivier
  • Maniquet, François


A social choice correspondence (SCC) is virtually implementable if it is [var epsilon]-close (in the probability simplex) to some (exactly) implementable correspondence [Abreu, D., Sen, A., 1991. Virtual Implementation in Nash Equilibrium. Econometrica 59, 997-1021] proved that, without restriction on the set of alternatives receiving strictly positive probability at equilibrium, every SCC is virtually implementable in Nash Equilibrium. We study virtual implementation when the supports of equilibrium lotteries are restricted. We provide a necessary and sufficient condition, imposing joint restrictions on SCCs and admissible supports. Next, we discuss how to construct supports, and we underline an important difficulty. Finally, we study virtual implementation when the support is restricted to the efficient or individually rational alternatives.

Suggested Citation

  • Bochet, Olivier & Maniquet, François, 2010. "Virtual Nash implementation with admissible support," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 99-108, January.
  • Handle: RePEc:eee:mateco:v:46:y:2010:i:1:p:99-108

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    References listed on IDEAS

    1. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
    2. François Maniquet, 2002. "A study of proportionality and robustness in economies with a commonly owned technology," Review of Economic Design, Springer;Society for Economic Design, vol. 7(1), pages 1-15.
    3. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer;Society for Economic Design, vol. 4(1), pages 13-33.
    4. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
    5. van Hoesel, C.P.M., 2005. "An overview of Stackelberg pricing in networks," Research Memorandum 036, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. Olivier Bochet, 2007. "Implementation of the Walrasian correspondence: the boundary problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 301-316, October.
    7. Jackson Matthew O. & Palfrey Thomas R. & Srivastava Sanjay, 1994. "Undominated Nash Implementation in Bounded Mechanisms," Games and Economic Behavior, Elsevier, vol. 6(3), pages 474-501, May.
    8. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Oxford University Press, vol. 59(4), pages 757-775.
    9. Demange, Gabrielle, 1984. "Implementing Efficient Egalitarian Equivalent Allocations," Econometrica, Econometric Society, vol. 52(5), pages 1167-1177, September.
    10. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
    11. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 111-125, January.
    12. Elisha A. Pazner & David Schmeidler, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, Oxford University Press, vol. 92(4), pages 671-687.
    13. 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.
    14. Vartiainen, Hannu, 2007. "Subgame perfect implementation: A full characterization," Journal of Economic Theory, Elsevier, vol. 133(1), pages 111-126, March.
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    Cited by:

    1. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    2. Artemov, Georgy, 2014. "An impossibility result for virtual implementation with status quo," Economics Letters, Elsevier, vol. 122(3), pages 380-385.
    3. İpek Özkal-Sanver & M. Sanver, 2010. "A new monotonicity condition for tournament solutions," Theory and Decision, Springer, vol. 69(3), pages 439-452, September.


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