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Universality of Nash Components

Author

Listed:
  • Dieter Balkenborg

    (Department of Economics, University of Exeter)

  • Dries Vermeulen

    (Department of Quantitative Economics, University Maastricht)

Abstract

We show that Nash equilibrium components are universal for the collection of connected polyhedral sets. More precisely for every polyhedral set we construct a so-called binary game — a common interest game whose common payoff to the players is at most equal to one—whose success set (the set of strategy profiles where the maximal payoff of one is indeed achieved) is homeomorphic to the given polyhedral set. Since compact semi-algebraic sets can be triangulated, a similar result follows for the collection of connected compact semi-algebraic sets.

Suggested Citation

  • Dieter Balkenborg & Dries Vermeulen, 2012. "Universality of Nash Components," Discussion Papers 1205, University of Exeter, Department of Economics.
    • Handle: RePEc:exe:wpaper:1205
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    File URL: https://exetereconomics.github.io/RePEc/dpapers/DP1205.pdf
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    References listed on IDEAS

    as
    1. Jean-François Mertens, 1989. "Stable Equilibria---A Reformulation," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 575-625, November.
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    3. McKelvey, Richard D. & McLennan, Andrew, 1997. "The Maximal Number of Regular Totally Mixed Nash Equilibria," Journal of Economic Theory, Elsevier, vol. 72(2), pages 411-425, February.
    4. Vermeulen, Dries & Jansen, Mathijs, 2005. "On the computation of stable sets for bimatrix games," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 735-763, September.
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    6. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    7. Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.
    8. MERTENS, Jean-François, 1991. "Stable equilibria - a reformulation. Part II. Discussion of the definition, and further results," LIDAM Reprints CORE 960, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Meroni, Claudia & Pimienta, Carlos, 2017. "The structure of Nash equilibria in Poisson games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 128-144.
    2. Balkenborg, Dieter & Vermeulen, Dries, 2019. "On the topology of the set of Nash equilibria," Games and Economic Behavior, Elsevier, vol. 118(C), pages 1-6.

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    More about this item

    Keywords

    Strategic form games; Nash equilibrium; Nash component; topology.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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