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On the topology of the set of Nash equilibria

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  • Balkenborg, Dieter
  • Vermeulen, Dries

Abstract

It has been an open conjecture in the theory of non-cooperative games that Nash equilibrium is universal for the collection of (non-empty) compact semi-algebraic sets, meaning that for every such set there is a game whose set of Nash equilibria is homeomorphic to the given set. In this paper we prove this conjecture.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:gamebe:v:118:y:2019:i:c:p:1-6
    DOI: 10.1016/j.geb.2019.08.008
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    References listed on IDEAS

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    8. Balkenborg, Dieter & Vermeulen, Dries, 2014. "Universality of Nash components," Games and Economic Behavior, Elsevier, vol. 86(C), pages 67-76.
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    Cited by:

    1. Levy, Yehuda John, 2022. "Uniformly supported approximate equilibria in families of games," Journal of Mathematical Economics, Elsevier, vol. 98(C).

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    More about this item

    Keywords

    Strategic form games; Nash equilibrium; 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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