Equilibrium selection in games: the mollifier method.

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    Abstract

    This paper introduces an embedding of a Nash equilibrium into a sequence of perturbed games, which achieves continuous differentiability of best responses by mollifying them over a continuously differentiable density with compact support (window size). Along any sequence with shrinking window size, the equilibria are single-valued whenever the function has a regular Jacobian and the set of equilibria where it is singular has measure zero. We achieve a further reduction of the equilibrium set by inserting within the embedding a procedure that eliminates the strict interior of equilibrium sets. The mollifier can be approximated consistently using kernel density regression, and we sketch a non-stationary stochastic optimization algorithm that uses this approximation and converges with probability one to an equilibrium of the original game. © 2003 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)285-301
    Number of pages17
    JournalJournal of Mathematical Economics
    Volume41
    Issue number3
    DOIs
    Publication statusPublished - 2005

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