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Generalized reinforcement learning in perfect-information games

Author

Listed:
  • Maxwell Pak

    () (Southwestern University of Finance and Economics)

  • Bing Xu

    () (Southwestern University of Finance and Economics)

Abstract

Abstract This paper studies reinforcement learning in which players base their action choice on valuations they have for the actions. We identify two general conditions on valuation updating rules that together guarantee that the probability of playing a subgame perfect Nash equilibrium (SPNE) converges to one in games where no player is indifferent between two outcomes without every other player being also indifferent. The same conditions guarantee that the fraction of times a SPNE is played converges to one almost surely. We also show that for additively separable valuations, in which valuations are the sum of empirical and error terms, the conditions guaranteeing convergence can be made more intuitive. In addition, we give four examples of valuations that satisfy our conditions. These examples represent different degrees of sophistication in learning behavior and include well-known examples of reinforcement learning.

Suggested Citation

  • Maxwell Pak & Bing Xu, 2016. "Generalized reinforcement learning in perfect-information games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 985-1011, November.
  • Handle: RePEc:spr:jogath:v:45:y:2016:i:4:d:10.1007_s00182-015-0499-1
    DOI: 10.1007/s00182-015-0499-1
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    References listed on IDEAS

    as
    1. Marx, Leslie M. & Swinkels, Jeroen M., 2000. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 31(2), pages 324-329, May.
    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. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    4. Jean-François Laslier & Bernard Walliser, 2005. "A reinforcement learning process in extensive form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 219-227, June.
    5. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
    6. Laslier, Jean-Francois & Topol, Richard & Walliser, Bernard, 2001. "A Behavioral Learning Process in Games," Games and Economic Behavior, Elsevier, vol. 37(2), pages 340-366, November.
    7. Sarin, Rajiv & Vahid, Farshid, 1999. "Payoff Assessments without Probabilities: A Simple Dynamic Model of Choice," Games and Economic Behavior, Elsevier, vol. 28(2), pages 294-309, August.
    8. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
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    More about this item

    Keywords

    Reinforcement learning; Extensive-form games;

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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