Virtual Nash Implementation with Admissible Support

CORE Discussion Paper No. 2006/84

21 Pages Posted: 5 Dec 2006

See all articles by Olivier Bochet

Olivier Bochet

New York University Abu Dhabi

Francois Maniquet

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE)

Date Written: August 2006

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.

Suggested Citation

Bochet, Olivier and Maniquet, Francois, Virtual Nash Implementation with Admissible Support (August 2006). CORE Discussion Paper No. 2006/84. Available at SSRN: https://ssrn.com/abstract=949155 or http://dx.doi.org/10.2139/ssrn.949155

Olivier Bochet (Contact Author)

New York University Abu Dhabi ( email )

PO Box 129188
Abu Dhabi
United Arab Emirates

HOME PAGE: http://https://sites.google.com/site/obochet2/

Francois Maniquet

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium
+32 10 474328 (Phone)
+32 10 474301 (Fax)

HOME PAGE: http://www.core.ucl.ac.be/staff/maniquetcore.htm

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