We provide a characterization of quasi-perfect equilibria in n-player games, 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, and any limit point of a sequence of Nash equilibria of these perturbed games is a quasi-perfect equilibrium. We prove that, in games with three or more players, we need trembles defined as rational functions of the perturbation magnitude ε, whereas, in two-player games with nature, trembles expressed in terms of polynomial functions of ε suffice. Exploiting the relationship between sequence form and extensive form, we also provide a similar characterization in terms of perturbed games in extensive form, though not compliant with Selten's definition of perturbed game.

Gatti, N., Gilli, M., & Marchesi, A. (2020). A characterization of quasi-perfect equilibria. GAMES AND ECONOMIC BEHAVIOR, 122, 240-255 [10.1016/j.geb.2020.04.012].

A characterization of quasi-perfect equilibria

Mario Gilli;
2020

Abstract

We provide a characterization of quasi-perfect equilibria in n-player games, 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, and any limit point of a sequence of Nash equilibria of these perturbed games is a quasi-perfect equilibrium. We prove that, in games with three or more players, we need trembles defined as rational functions of the perturbation magnitude ε, whereas, in two-player games with nature, trembles expressed in terms of polynomial functions of ε suffice. Exploiting the relationship between sequence form and extensive form, we also provide a similar characterization in terms of perturbed games in extensive form, though not compliant with Selten's definition of perturbed game.
Articolo in rivista - Articolo scientifico
Scientifica
Characterization; Games in sequence form; Quasi-perfect equilibrium; Trembles;
English
Gatti, N., Gilli, M., & Marchesi, A. (2020). A characterization of quasi-perfect equilibria. GAMES AND ECONOMIC BEHAVIOR, 122, 240-255 [10.1016/j.geb.2020.04.012].
Gatti, N; Gilli, M; Marchesi, A
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/274091
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