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The dynamics of generalized reinforcement learning

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  • Lahkar, Ratul
  • Seymour, Robert M.

Abstract

We consider reinforcement learning in games with both positive and negative payoffs. The Cross rule is the prototypical reinforcement learning rule in games that have only positive payoffs. We extend this rule to incorporate negative payoffs to obtain the generalized reinforcement learning rule. Applying this rule to a population game, we obtain the generalized reinforcement dynamic which describes the evolution of mixed strategies in the population. We apply the dynamic to the class of Rock–Scissor–Paper (RSP) games to establish local convergence to the interior rest point in all such games, including the bad RSP game.

Suggested Citation

  • Lahkar, Ratul & Seymour, Robert M., 2014. "The dynamics of generalized reinforcement learning," Journal of Economic Theory, Elsevier, vol. 151(C), pages 584-595.
    • Handle: RePEc:eee:jetheo:v:151:y:2014:i:c:p:584-595
    DOI: 10.1016/j.jet.2014.01.002
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    References listed on IDEAS

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    Cited by:

    1. Schauf, Andrew & Oh, Poong, 2021. "Adaptation strategies and collective dynamics of extraction in networked commons of bistable resources," SocArXiv wmtqk, Center for Open Science.
    2. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    3. Lahkar, Ratul, 2017. "Equilibrium selection in the stag hunt game under generalized reinforcement learning," Journal of Economic Behavior & Organization, Elsevier, vol. 138(C), pages 63-68.
    4. Funai, Naoki, 2022. "Reinforcement learning with foregone payoff information in normal form games," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 638-660.

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    More about this item

    Keywords

    Reinforcement learning; Negative reinforcement; Replicator dynamic;
    All these keywords.

    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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