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Refinements of Nash equilibrium in potential games

Author

Listed:
  • Oriol Carbonell-Nicolau

    (Rutgers University)

  • Richard McLean

    (Rutgers University)

Abstract

We prove the existence of strategically stable sets of pure-strategy Nash equilibria (and hence the existence of pure-strategy trembling-hand perfect equilibria) in potential games that admit an upper semicontinuous potential, and we show that generic potential games possess pure-strategy strictly perfect and essential equilibria. In addition, we provide a link between upper semicontinuity of a potential and conditions defined directly on the payo ff functions of a potential game. Finally, we show that stable sets and (strictly) perfect equilibria are related to the set of maximizers of a potential, which refines the set of Nash equilibria. Specifically, the set of maximizers of a potential contains a strategically stable set of pure-strategy Nash equilibria (and hence a pure-strategy trembling-hand perfect equilibrium) and, for generic games, any maximizer of a potential is a pure-strategy strictly perfect and essential equilibrium.

Suggested Citation

  • Oriol Carbonell-Nicolau & Richard McLean, 2011. "Refinements of Nash equilibrium in potential games," Departmental Working Papers 201125, Rutgers University, Department of Economics.
    • Handle: RePEc:rut:rutres:201125
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    References listed on IDEAS

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    9. Oriol Carbonell-Nicolau, 2021. "Perfect equilibria in games of incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1591-1648, June.
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    11. Argyrios Deligkas & Eduard Eiben & Gregory Gutin & Philip R. Neary & Anders Yeo, 2023. "Some coordination problems are harder than others," Papers 2311.03195, arXiv.org, revised Nov 2023.

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    More about this item

    Keywords

    discontinuous game; potential game; trembling-hand perfect equilibrium; stable set; essential equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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