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Nonconvergence to saddle boundary points under perturbed reinforcement learning

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  • Georgios Chasparis
  • Jeff Shamma
  • Anders Rantzer

Abstract

For several reinforcement learning models in strategic-form games, convergence to action profiles that are not Nash equilibria may occur with positive probability under certain conditions on the payoff function. In this paper, we explore how an alternative reinforcement learning model, where the strategy of each agent is perturbed by a strategy-dependent perturbation (or mutations) function, may exclude convergence to non-Nash pure strategy profiles. This approach extends prior analysis on reinforcement learning in games that addresses the issue of convergence to saddle boundary points. It further provides a framework under which the effect of mutations can be analyzed in the context of reinforcement learning. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Georgios Chasparis & Jeff Shamma & Anders Rantzer, 2015. "Nonconvergence to saddle boundary points under perturbed reinforcement learning," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 667-699, August.
    • Handle: RePEc:spr:jogath:v:44:y:2015:i:3:p:667-699
    DOI: 10.1007/s00182-014-0449-3
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    References listed on IDEAS

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    1. Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207.
    2. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    3. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
    4. Cho, In-Koo & Matsui, Akihiko, 2005. "Learning aspiration in repeated games," Journal of Economic Theory, Elsevier, vol. 124(2), pages 171-201, October.
    5. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
    6. Hopkins, Ed & Posch, Martin, 2005. "Attainability of boundary points under reinforcement learning," Games and Economic Behavior, Elsevier, vol. 53(1), pages 110-125, October.
    7. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    8. Arthur, W Brian, 1993. "On Designing Economic Agents That Behave Like Human Agents," Journal of Evolutionary Economics, Springer, vol. 3(1), pages 1-22, February.
    9. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
    10. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
    11. Bonacich, Phillip & Liggett, Thomas M., 2003. "Asymptotics of a matrix valued Markov chain arising in sociology," Stochastic Processes and their Applications, Elsevier, vol. 104(1), pages 155-171, March.
    12. Georgios Chasparis & Jeff Shamma, 2012. "Distributed Dynamic Reinforcement of Efficient Outcomes in Multiagent Coordination and Network Formation," Dynamic Games and Applications, Springer, vol. 2(1), pages 18-50, March.
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    More about this item

    Keywords

    Learning in games; Reinforcement learning; Replicator dynamics; C72; C73; D83;
    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
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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