Equilibrium selection in games: the mollifier method.

    Research output: Contribution to JournalArticleAcademic

    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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    Equilibrium Selection
    Game
    Singular Measures
    Kernel Density
    Single valued
    Stochastic Algorithms
    Continuously differentiable
    Stochastic Optimization
    Compact Support
    Shrinking
    Differentiability
    Nash Equilibrium
    Optimization Algorithm
    Interior
    Eliminate
    Regression
    Equilibrium selection
    Converge
    Zero
    Approximation

    Cite this

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    title = "Equilibrium selection in games: the mollifier method.",
    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. {\circledC} 2003 Elsevier B.V. All rights reserved.",
    author = "M.A. Keyzer and {van Wesenbeeck}, C.F.A.",
    year = "2005",
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    Equilibrium selection in games: the mollifier method. / Keyzer, M.A.; van Wesenbeeck, C.F.A.

    In: Journal of Mathematical Economics, Vol. 41, No. 3, 2005, p. 285-301.

    Research output: Contribution to JournalArticleAcademic

    TY - JOUR

    T1 - Equilibrium selection in games: the mollifier method.

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    AU - van Wesenbeeck, C.F.A.

    PY - 2005

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    N2 - 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.

    AB - 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.

    U2 - 10.1016/j.jmateco.2003.10.005

    DO - 10.1016/j.jmateco.2003.10.005

    M3 - Article

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