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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 [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.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers RP with number -2228.

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Handle: RePEc:cor:louvrp:-2228

Note: In : Journal of Mathematical Economics, 46(1), 99-108, 2010
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  1. Bochet,Olivier, 2005. "Implementation of the Walrasian Correspondence: The Boundary Problem," Research Memorandum 037, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Bochet,Olivier, 2005. "Nash Implementation with Lottery Mechanisms," Research Memorandum 036, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  3. Thomson, W., 1996. "Monotonic Extension on Economic Domains," RCER Working Papers 431, University of Rochester - Center for Economic Research (RCER).
  4. 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.
  5. Vartiainen, Hannu, 2007. "Subgame perfect implementation: A full characterization," Journal of Economic Theory, Elsevier, vol. 133(1), pages 111-126, March.
  6. Olivier Bochet, 2007. "Implementation of the Walrasian correspondence: the boundary problem," International Journal of Game Theory, Springer, vol. 36(2), pages 301-316, October.
  7. François Maniquet, 2002. "A study of proportionality and robustness in economies with a commonly owned technology," Review of Economic Design, Springer, vol. 7(1), pages 1-15.
  8. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer, vol. 28(1), pages 111-125, January.
  9. Demange, Gabrielle, 1984. "Implementing Efficient Egalitarian Equivalent Allocations," Econometrica, Econometric Society, vol. 52(5), pages 1167-77, September.
  10. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  11. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
  12. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  13. Matthew O. Jackson, 1990. "Undominated Nash Implementation in Bounded Mechanisms," Discussion Papers 966, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Jackson, Matthew O, 1992. "Implementation in Undominated.Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 59(4), pages 757-75, October.
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Cited by:
  1. İpek Özkal-Sanver & M. Sanver, 2010. "A new monotonicity condition for tournament solutions," Theory and Decision, Springer, vol. 69(3), pages 439-452, September.
  2. Claudio Mezzetti & Ludovic Renou, 2009. "Implementation in Mixed Nash Equilibrium," Discussion Papers in Economics 09/10, Department of Economics, University of Leicester, revised Jan 2010.

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