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On the robustness of learning in games with stochastically perturbed payoff observations

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  • Bravo, Mario
  • Mertikopoulos, Panayotis

Abstract

Motivated by the scarcity of accurate payoff feedback in practical applications of game theory, we examine a class of learning dynamics where players adjust their choices based on past payoff observations that are subject to noise and random disturbances. First, in the single-player case (corresponding to an agent trying to adapt to an arbitrarily changing environment), we show that the stochastic dynamics under study lead to no regret almost surely, irrespective of the noise level in the player's observations. In the multi-player case, we find that dominated strategies become extinct and we show that strict Nash equilibria are stochastically stable and attracting; conversely, if a state is stable or attracting with positive probability, then it is a Nash equilibrium. Finally, we provide an averaging principle for 2-player games, and we show that in zero-sum games with an interior equilibrium, time averages converge to Nash equilibrium for any noise level.

Suggested Citation

  • Bravo, Mario & Mertikopoulos, Panayotis, 2017. "On the robustness of learning in games with stochastically perturbed payoff observations," Games and Economic Behavior, Elsevier, vol. 103(C), pages 41-66.
    • Handle: RePEc:eee:gamebe:v:103:y:2017:i:c:p:41-66
    DOI: 10.1016/j.geb.2016.06.004
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    Cited by:

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    4. Masiliūnas, Aidas, 2023. "Learning in rent-seeking contests with payoff risk and foregone payoff information," Games and Economic Behavior, Elsevier, vol. 140(C), pages 50-72.

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    More about this item

    Keywords

    Dominated strategies; Learning; Nash equilibrium; Regret minimization; Regularization; Robustness; Stochastic game dynamics; Stochastic stability;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • 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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