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
    StatePublished - Jan 20 2010

    Fingerprint

    Social Choice
    Correspondence
    Nash Equilibrium
    Restriction
    Lottery
    Alternatives
    Strictly positive
    Necessary Conditions
    Sufficient Conditions
    Virtual implementation
    Nash implementation
    Social choice correspondence
    Nash equilibrium

    Keywords

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

    ASJC Scopus subject areas

    • Economics and Econometrics
    • Applied Mathematics

    Cite this

    Virtual Nash implementation with admissible support. / Bochet, Olivier; Maniquet, François.

    In: Journal of Mathematical Economics, Vol. 46, No. 1, 20.01.2010, p. 99-108.

    Research output: Contribution to journalArticle

    Bochet, Olivier ; Maniquet, François. / Virtual Nash implementation with admissible support. In: Journal of Mathematical Economics. 2010 ; Vol. 46, No. 1. pp. 99-108.
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