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Sequential Equilibria in Mixed Strategies

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  • Francesc Dilmé

Abstract

A Nash equilibrium of a game in extensive form is a sequential equilibrium in mixed strategies if it can be approximated through equilibria of close-by games with slightly perturbed payoffs and small-probability behavioral types. We show that sequential equilibria in mixed strategies are equivalent to (i) weakly sequential equilibria (Reny, 1992), (ii) normal-form perfect equilibria (Selten, 1975) in games with generic payoffs, and (iii) purifiable Nash equilibria (Harsanyi, 1973). A corollary of our results is that extensive-form perfect equilibria are normal-form perfect equilibria in games with generic payoffs.

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  • Francesc Dilmé, 2025. "Sequential Equilibria in Mixed Strategies," CRC TR 224 Discussion Paper Series crctr224_2025_703, University of Bonn and University of Mannheim, Germany.
    • Handle: RePEc:bon:boncrc:crctr224_2025_703
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    1. van Damme, E.E.C., 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Other publications TiSEM 3734d89e-fd5c-4c80-a230-5, Tilburg University, School of Economics and Management.
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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