On the Characterization of Quasi-Perfect Equilibria

38 Pages Posted: 8 Nov 2018

See all articles by Nicola Gatti

Nicola Gatti

Polytechnic University of Milan

Mario Gilli

Università degli Studi di Milano-Bicocca - Center for Interdisciplinary Studies in Economics, Psychology & Social Sciences (CISEPS); Università degli Studi di Milano-Bicocca - Department of Economics, Management and Statistics (DEMS)

Alberto Marchesi

Polytechnic University of Milan

Date Written: November 2, 2018

Abstract

Van Damme [1984] introduces the concept of quasi-perfect equilibrium, which re-fines 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 Sørensen [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.

JEL Classification: C70, C72

Suggested Citation

Gatti, Nicola and Gilli, Mario and Marchesi, Alberto, On the Characterization of Quasi-Perfect Equilibria (November 2, 2018). University of Milan Bicocca Department of Economics, Management and Statistics Working Paper No. 389, Available at SSRN: https://ssrn.com/abstract=3277293 or http://dx.doi.org/10.2139/ssrn.3277293

Nicola Gatti

Polytechnic University of Milan ( email )

Piazza Leonardo da Vinci
Milan, Milano 20100
Italy

Mario Gilli (Contact Author)

Università degli Studi di Milano-Bicocca - Center for Interdisciplinary Studies in Economics, Psychology & Social Sciences (CISEPS) ( email )

Piazza dell'Ateneo Nuovo, 1
Milano, 20126
Italy

Università degli Studi di Milano-Bicocca - Department of Economics, Management and Statistics (DEMS) ( email )

Piazza dell'Ateneo Nuovo, 1
Milan, 20126
Italy

Alberto Marchesi

Polytechnic University of Milan ( email )

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