On the Characterization of Quasi-Perfect Equilibria
University of Milan Bicocca Department of Economics, Management and Statistics Working Paper No. 389
38 Pages Posted: 8 Nov 2018
Date Written: November 2, 2018
Van Damme  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  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 , 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: Suggested Citation