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On the characterization of quasi-perfect equilibria

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  • Nicola, Gatti
  • Mario, Gilli
  • Alberto, Marchesi

Abstract

Van Damme [1984] introduces the concept of quasi-perfect equilibrium, which refines sequential equilibrium as well as normal-form perfect equilibrium. It has been argued by Mertens [1995] that quasi-perfection is conceptually superior to extensive- form perfection, since quasi-perfection guarantees normal-form perfection, which for two-player games is equivalent to admissibility. On the other hand, while extensive-form perfect equilibria are defined as limit points of sequences of Nash equilibria of a general class of perturbed games in extensive form, till now, to the best of our knowledge, there is no characterization of quasi-perfect equilibria in terms of limit points of equilibria of perturbed games. The only known result is Lemma 1 by Miltersen and Sorensen [2010], showing that limit points of sequences of Nash equilibria of a particular class of perturbed games in sequence form are quasi-perfect equilibria of the original, unperturbed game in extensive form. However, as the authors point out, their main result only proves that a subset of the quasi-perfect equilibria can be obtained as limit points of equilibria of their class of perturbed games, and, thus, their paper provides no characterization of quasi-perfect equilibria in terms of perturbed games. The present paper fills this gap providing such characterization, showing that any quasi-perfect equilibrium can be obtained as limit point of a sequence of Nash equilibria of a certain class of perturbed games in sequence form, at least for the case of two-player games with nature. This result shows that the sequence form is not merely a computationally efficient representation, but it also captures game features that other forms are not able to effectively express.

Suggested Citation

  • Nicola, Gatti & Mario, Gilli & Alberto, Marchesi, 2018. "On the characterization of quasi-perfect equilibria," Working Papers 389, University of Milano-Bicocca, Department of Economics, revised 07 Nov 2018.
  • Handle: RePEc:mib:wpaper:389
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    References listed on IDEAS

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    1. Srihari Govindan & Robert Wilson, 2012. "Axiomatic Equilibrium Selection for Generic Two‐Player Games," Econometrica, Econometric Society, vol. 80(4), pages 1639-1699, July.
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    More about this item

    Keywords

    Non-cooperative Game Theory; Extensive Games; Nash Equilibrium Refinements;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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