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Reinforcement learning in population games

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  • Lahkar, Ratul
  • Seymour, Robert M.
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 80 (2013)
    Issue (Month): C ()
    Pages: 10-38

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    Handle: RePEc:eee:gamebe:v:80:y:2013:i:c:p:10-38

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    Web page: http://www.elsevier.com/locate/inca/622836

    Related research

    Keywords: Reinforcement learning; Continuity equation; Replicator dynamics;

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    1. Friedman, Daniel & Ostrov, Daniel N., 2010. "Gradient dynamics in population games: Some basic results," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 691-707, September.
    2. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
    3. Ellison, Glenn & Fudenberg, Drew, 2000. "Learning Purified Mixed Equilibria," Journal of Economic Theory, Elsevier, vol. 90(1), pages 84-115, January.
    4. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    5. Josef Hofbauer & Sylvain Sorin & Yannick Viossat, 2009. "Time Average Replicator and Best Reply Dynamics," Post-Print hal-00360767, HAL.
    6. Borgers, Tilman & Sarin, Rajiv, 2000. "Naive Reinforcement Learning with Endogenous Aspirations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 921-50, November.
    7. Ed Hopkins, . "Learning, Matching and Aggregation," ESE Discussion Papers 2, Edinburgh School of Economics, University of Edinburgh.
    8. Tilman Börgers & Antonio J. Morales & Rajiv Sarin, 2004. "Expedient and Monotone Learning Rules," Econometrica, Econometric Society, vol. 72(2), pages 383-405, 03.
    9. Fudenberg, Drew & Takahashi, Satoru, 2011. "Heterogeneous beliefs and local information in stochastic fictitious play," Games and Economic Behavior, Elsevier, vol. 71(1), pages 100-120, January.
    10. S. Hart & A. Mas-Collel, 2010. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Levine's Working Paper Archive 572, David K. Levine.
    11. Ramsza, Michal & Seymour, Robert M., 2010. "Fictitious play in an evolutionary environment," Games and Economic Behavior, Elsevier, vol. 68(1), pages 303-324, January.
    12. Hofbauer, Josef & Sandholm, William H., 2009. "Stable games and their dynamics," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1665-1693.e, July.
    13. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-81, September.
    14. Ely, Jeffrey C. & Sandholm, William H., 2005. "Evolution in Bayesian games I: Theory," Games and Economic Behavior, Elsevier, vol. 53(1), pages 83-109, October.
    15. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
    16. Friedman, Daniel & Ostrov, Daniel N., 2008. "Conspicuous consumption dynamics," Games and Economic Behavior, Elsevier, vol. 64(1), pages 121-145, September.
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