Virtual Nash implementation with admissible support

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Virtual Nash implementation with admissible support

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BOCHET, Olivier
MANIQUET, Franois

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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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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2006084.

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Date of creation: 01 Oct 2006
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Handle: RePEc:cor:louvco:2006084

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Paper
- Olivier, BOCHET & Franois, MANIQUET, 2006. "Virtual Nash implementation with admissible support," Discussion Papers (ECON - DÃ©partement des Sciences Economiques) 2006043, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]

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Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June. [Downloadable!] (restricted)
Demange, Gabrielle, 1984. "Implementing Efficient Egalitarian Equivalent Allocations," Econometrica, Econometric Society, vol. 52(5), pages 1167-77, September. [Downloadable!] (restricted)
BOCHET, Olivier, 2005. "Implementation of the Walrasian correspondence: the boundary problem," CORE Discussion Papers 2005060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
Other versions:
- Bochet,Olivier, 2005. "Implementation of the Walrasian Correspondence: The Boundary Problem," Research Memoranda 037, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
- Olivier Bochet, 2007. "Implementation of the Walrasian correspondence: the boundary problem," International Journal of Game Theory, Springer, vol. 36(2), pages 301-316, October. [Downloadable!] (restricted)
Jackson, Matthew O, 1992. "Implementation in Undominated.Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Blackwell Publishing, vol. 59(4), pages 757-75, October. [Downloadable!] (restricted)
Other versions:
- Matthew 0. Jackson, 1989. "Implementation in Undominated Strategies - A Look at Bounded Mechanisms," Discussion Papers 833, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September. [Downloadable!] (restricted)
Vartiainen, Hannu, 2007. "Subgame perfect implementation: A full characterization," Journal of Economic Theory, Elsevier, vol. 133(1), pages 111-126, March. [Downloadable!] (restricted)
BOCHET, Olivier, 2005. "Nash implementation with lottery mechanisms," CORE Discussion Papers 2005072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
Other versions:
- Bochet,Olivier, 2005. "Nash Implementation with Lottery Mechanisms," Research Memoranda 036, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
- Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer, vol. 28(1), pages 111-125, January. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)
William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer, vol. 4(1), pages 13-33. [Downloadable!] (restricted)
Other versions:
- Thomson, W., 1996. "Monotonic Extension on Economic Domains," RCER Working Papers 431, University of Rochester - Center for Economic Research (RCER).
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. [Downloadable!] (restricted)
Other versions:
- Matthew, Jackson O. & Palfrey, Thomas R. & Srivastava, Sanjay., 1990. "Undominated Nash Implementation in Bounded Mechanism," Working Papers 754, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
- Matthew O. Jackson, 1990. "Undominated Nash Implementation in Bounded Mechanisms," Discussion Papers 966, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July. [Downloadable!] (restricted)
Other versions:
- Abreu, D. & Sen, A., 1989. "Virtual Implementation In Nash Equilibrium," Papers e-90-13, Stanford - Hoover Institution.

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Veiga, Helena & Vorsatz, Marc, 2006. "Price Manipulation in an Experimental Asset Market," Research Memoranda 024, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
Other versions:
- Veiga, Helena & Vorsatz, Marc, 2009. "Price manipulation in an experimental asset market," European Economic Review, Elsevier, vol. 53(3), pages 327-342, April. [Downloadable!] (restricted)

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