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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

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 46 (2010)
Issue (Month): 1 (January)
Pages: 99-108

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Handle: RePEc:eee:mateco:v:46:y:2010:i:1:p:99-108

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Virtual implementation Admissible support Extended monotonicity Maskin monotonicity;

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References

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  1. Jackson Matthew O. & Palfrey Thomas R. & Srivastava Sanjay, 1994. "Undominated Nash Implementation in Bounded Mechanisms," Games and Economic Behavior, Elsevier, Elsevier, vol. 6(3), pages 474-501, May.
  2. BOCHET, Olivier, 2005. "Nash implementation with lottery mechanisms," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2005072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Demange, Gabrielle, 1984. "Implementing Efficient Egalitarian Equivalent Allocations," Econometrica, Econometric Society, Econometric Society, vol. 52(5), pages 1167-77, September.
  4. François Maniquet, 2002. "A study of proportionality and robustness in economies with a commonly owned technology," Review of Economic Design, Springer, Springer, vol. 7(1), pages 1-15.
  5. Thomson, W., 1996. "Monotonic Extension on Economic Domains," RCER Working Papers, University of Rochester - Center for Economic Research (RCER) 431, University of Rochester - Center for Economic Research (RCER).
  6. Pazner, Elisha A & Schmeidler, David, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 92(4), pages 671-87, November.
  7. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, Econometric Society, vol. 56(5), pages 1191-1220, September.
  8. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 59(4), pages 997-1021, July.
  9. Bochet,Olivier, 2005. "Nash Implementation with Lottery Mechanisms," Research Memorandum, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) 036, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  10. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, Elsevier, vol. 45(1), pages 128-144, June.
  11. Abreu, Dilip & Sen, Arunava, 1990. "Subgame perfect implementation: A necessary and almost sufficient condition," Journal of Economic Theory, Elsevier, Elsevier, vol. 50(2), pages 285-299, April.
  12. Vartiainen, Hannu, 2007. "Subgame perfect implementation: A full characterization," Journal of Economic Theory, Elsevier, Elsevier, vol. 133(1), pages 111-126, March.
  13. BOCHET, Olivier, 2005. "Implementation of the Walrasian correspondence: the boundary problem," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2005060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Matthew 0. Jackson, 1989. "Implementation in Undominated Strategies - A Look at Bounded Mechanisms," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 833, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. Bochet,Olivier, 2005. "Implementation of the Walrasian Correspondence: The Boundary Problem," Research Memorandum, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) 037, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
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Citations

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Cited by:
  1. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, Elsevier, vol. 147(6), pages 2357-2375.
  2. Artemov, Georgy, 2014. "An impossibility result for virtual implementation with status quo," Economics Letters, Elsevier, 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, Springer, vol. 69(3), pages 439-452, September.

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