Effects of noise on convergent game-learning dynamics

James B T Sanders, Tobias Galla, Jonathan L. Shapiro

    Research output: Contribution to journalArticlepeer-review


    We study stochastic effects on the lagging anchor dynamics, a reinforcement learning algorithm used to learn successful strategies in iterated games, which is known to converge to Nash points in the absence of noise. The dynamics is stochastic when players only have limited information about their opponents strategic propensities. The effects of this noise are studied analytically in the case where it is small but finite, and we show that the statistics and correlation properties of fluctuations can be computed to a high accuracy. We find that the system can exhibit quasicycles, driven by intrinsic noise. If players are asymmetric and use different parameters for their learning, a net payoff advantage can be achieved due to these stochastic oscillations around the deterministic equilibrium. © 2012 IOP Publishing Ltd.
    Original languageEnglish
    Article number105001
    JournalJournal of Physics A: Mathematical and Theoretical
    Issue number10
    Publication statusPublished - 16 Mar 2012


    • Decision theory
    • Game theory
    • Stochastic processes
    • Stochastic games
    • Computational Physics


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