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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 ε-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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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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References

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  1. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, Econometric Society, vol. 56(5), pages 1191-1220, September.
  2. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 59(4), pages 997-1021, July.
  3. 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).
  4. Elisha A. Pazner & David Schmeidler, 1975. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 174, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. 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).
  6. 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.
  7. 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.
  8. 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.
  9. 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).
  10. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer, Springer, vol. 4(1), pages 13-33.
  11. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, Elsevier, vol. 45(1), pages 128-144, June.
  12. Bochet,Olivier, 2005. "Nash Implementation with Lottery Mechanisms," Research Memorandum 036, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  13. Vartiainen, Hannu, 2007. "Subgame perfect implementation: A full characterization," Journal of Economic Theory, Elsevier, Elsevier, vol. 133(1), pages 111-126, March.
  14. Demange, Gabrielle, 1984. "Implementing Efficient Egalitarian Equivalent Allocations," Econometrica, Econometric Society, Econometric Society, vol. 52(5), pages 1167-77, September.
  15. 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.
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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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