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Reinforcement learning in population games

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  • Lahkar, Ratul
  • Seymour, Robert M.

Abstract

We study reinforcement learning in a population game. Agents in a population game revise mixed strategies using the Cross rule of reinforcement learning. The population state—the probability distribution over the set of mixed strategies—evolves according to the replicator continuity equation which, in its simplest form, is a partial differential equation. The replicator dynamic is a special case in which the initial population state is homogeneous, i.e. when all agents use the same mixed strategy. We apply the continuity dynamic to various classes of symmetric games. Using 3×3 coordination games, we show that equilibrium selection depends on the variance of the initial strategy distribution, or initial population heterogeneity. We give an example of a 2×2 game in which heterogeneity persists even as the mean population state converges to a mixed equilibrium. Finally, we apply the dynamic to negative definite and doubly symmetric games.

Suggested Citation

  • Lahkar, Ratul & Seymour, Robert M., 2013. "Reinforcement learning in population games," Games and Economic Behavior, Elsevier, vol. 80(C), pages 10-38.
  • Handle: RePEc:eee:gamebe:v:80:y:2013:i:c:p:10-38
    DOI: 10.1016/j.geb.2013.02.006
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    Citations

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    Cited by:

    1. Dai Zusai, 2018. "Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution," Papers 1805.04897, arXiv.org, revised May 2019.
    2. Lahkar, Ratul & Seymour, Robert M., 2014. "The dynamics of generalized reinforcement learning," Journal of Economic Theory, Elsevier, vol. 151(C), pages 584-595.
    3. Dai Zusai, 2017. "Nonaggregable evolutionary dynamics under payoff heterogeneity," DETU Working Papers 1702, Department of Economics, Temple University.
    4. Wei, Fangfang & Jia, Ning & Ma, Shoufeng, 2016. "Day-to-day traffic dynamics considering social interaction: From individual route choice behavior to a network flow model," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 335-354.
    5. V'ictor Gallego & Roi Naveiro & David R'ios Insua & Wolfram Rozas, 2021. "Data sharing games," Papers 2101.10721, arXiv.org.
    6. Lai, Chong & Li, Rui & Gao, Xiujuan, 2024. "Bank competition with technological innovation based on evolutionary games," International Review of Economics & Finance, Elsevier, vol. 89(PA), pages 742-759.

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    More about this item

    Keywords

    Reinforcement learning; Continuity equation; Replicator dynamics;
    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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