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Virtual Nash implementation with admissible support

Author

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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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    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. 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).
    4. Jain, Ritesh, 2021. "Rationalizable implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 127(C), pages 47-66.
    5. Matias Nunez & M. Remzi Sanver, 2021. "On the subgame perfect implementability of voting rules," Post-Print hal-03341697, HAL.
    6. Anand Chopra & Malachy James Gavan & Antonio Penta, 2025. "Safe implementation in mixed nash equilibrium," Economics Working Papers 1911, Department of Economics and Business, Universitat Pompeu Fabra.
    7. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    8. Artemov, Georgy, 2014. "An impossibility result for virtual implementation with status quo," Economics Letters, Elsevier, vol. 122(3), pages 380-385.
    9. İpek Özkal-Sanver & M. Sanver, 2010. "A new monotonicity condition for tournament solutions," Theory and Decision, Springer, vol. 69(3), pages 439-452, September.
    10. Chopra, Anand & Gavan, Malachy James & Penta, Antonio, 2026. "Safe implementation in mixed Nash equilibrium," Journal of Mathematical Economics, Elsevier, vol. 122(C).

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