Virtual Nash implementation with admissible support

Olivier Bochet () and Francois Paul Maniquet ()

No 2006084, CORE Discussion Papers from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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.

Date: Written
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Working Paper: Virtual Nash implementation with admissible support (2006)
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