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Refinements of Nash equilibrium in potential games

Author

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  • 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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    3. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
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    Cited by:

    1. Vincent Boucher, 2017. "Selecting Equilibria using Best-Response Dynamics," Economics Bulletin, AccessEcon, vol. 37(4), pages 2728-2734.
    2. Boucher, Vincent, 2016. "Conformism and self-selection in social networks," Journal of Public Economics, Elsevier, vol. 136(C), pages 30-44.
    3. Laurent Lamy & Philippe Jehiel, 2016. "On the benefits of set-asides," Post-Print hal-01688237, HAL.

    More about this item

    Keywords

    discontinuous game; potential game; trembling-hand perfect equilibrium; stable set; essential equilibrium;

    JEL classification:

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

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