Virtual Nash implementation with admissible support

Olivier Bochet, François Maniquet

Research output: Contribution to journalArticle

Abstract

A social choice correspondence (SCC) is virtually implementable if it is ε-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.

Original languageEnglish (US)
Pages (from-to)99-108
Number of pages10
JournalJournal of Mathematical Economics
Volume46
Issue number1
DOIs
Publication statusPublished - Jan 20 2010

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Keywords

  • Admissible support
  • Extended monotonicity
  • Maskin monotonicity
  • Virtual implementation

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics

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