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Virtual Nash implementation with admissible support

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  • BOCHET, Olivier
  • MANIQUET, François

Abstract

A social choice correspondence (SCC) is virtually implementable if it is e-close (in the probability simplex) to some (exactly) implementable correspondence. Abreu and Sen (1991) 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. Then, we discuss how to construct supports. Finally, we study virtual implementation when the support is restricted to the efficient or individually rational alternatives.
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Suggested Citation

  • BOCHET, Olivier & MANIQUET, François, 2010. "Virtual Nash implementation with admissible support," LIDAM Reprints CORE 2228, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2228
    DOI: 10.1016/j.jmateco.2009.06.011
    Note: In : Journal of Mathematical Economics, 46(1), 99-108, 2010
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    References listed on IDEAS

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    1. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
    2. 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.
    3. 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.
    4. Bochet, Olivier, 2007. "Switching from complete to incomplete information," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 735-748, August.
    5. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer;Society for Economic Design, vol. 4(1), pages 13-33.
    6. 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.
    7. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
    8. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(4), pages 757-775.
    9. 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).
    10. Elisha A. Pazner & David Schmeidler, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 92(4), pages 671-687.
    11. 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.
    12. 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.
    13. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    14. Demange, Gabrielle, 1984. "Implementing Efficient Egalitarian Equivalent Allocations," Econometrica, Econometric Society, vol. 52(5), pages 1167-1177, September.
    15. Vartiainen, Hannu, 2007. "Subgame perfect implementation: A full characterization," Journal of Economic Theory, Elsevier, vol. 133(1), pages 111-126, March.
    16. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
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    Cited by:

    1. Margarita Kirneva & Matias Nunez, 2021. "Voting by Simultaneous Vetoes," Working Papers 2021-08, Center for Research in Economics and Statistics.
    2. Matías Núñez & M. Remzi Sanver, 2021. "On the subgame perfect implementability of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 421-441, February.
    3. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    4. Laslier, Jean-François & Núñez, Matías & Remzi Sanver, M., 2021. "A solution to the two-person implementation problem," Journal of Economic Theory, Elsevier, vol. 194(C).
    5. Matias Nunez & M. Remzi Sanver, 2021. "On the subgame perfect implementability of voting rules," Post-Print hal-03341697, HAL.
    6. Jain, Ritesh, 2021. "Rationalizable implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 127(C), pages 47-66.
    7. Artemov, Georgy, 2014. "An impossibility result for virtual implementation with status quo," Economics Letters, Elsevier, vol. 122(3), pages 380-385.
    8. 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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