On the characterization of quasi-perfect equilibria

Nicola, Gatti, Mario Gilli and Alberto, Marchesi

No 389, Working Papers from University of Milano-Bicocca, Department of Economics

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.

Keywords: Non-cooperative Game Theory; Extensive Games; Nash Equilibrium Refinements (search for similar items in EconPapers)
JEL-codes: C70 C72 (search for similar items in EconPapers)
Pages: 38
Date: 2018-11-07, Revised 2018-11-07
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-mic
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Journal Article: A characterization of quasi-perfect equilibria (2020)
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