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Sequential Equilibria in Mixed Strategies

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  • Francesc Dilmé

    (University of Bonn)

Abstract

We analyze limiting equilibrium behavior along perturbations of a game in which both nature and strategic players tremble with small probability. We show that allowing nature to tremble to zero-probability actions expands the set of sequential equilibria and contracts the set of sequentially stable outcomes while preserving their existence. By extending a game through adding initial zero-probability moves by nature, we identify conditions for the existence of reputation effects, that is, changes in the model’s predictions due to the presence of payoff types. Finally, we discuss the relationship between reputation effects and forward induction arguments

Suggested Citation

  • Francesc Dilmé, 2025. "Sequential Equilibria in Mixed Strategies," ECONtribute Discussion Papers Series 373, University of Bonn and University of Cologne, Germany.
    • Handle: RePEc:ajk:ajkdps:373
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    File URL: https://www.econtribute.de/RePEc/ajk/ajkdps/ECONtribute_373_2025.pdf
    File Function: First version, 2025
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    References listed on IDEAS

    as
    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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