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Probability Matching and Reinforcement Learning

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  • Javier Rivas

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Abstract

Probability matching occurs when an action is chosen with a frequency equivalent to the probability of that action being the best choice. This sub-optimal behavior has been reported repeatedly by psychologist and experimental economist. We provide an evolutionary foundation for this phenomenon by showing that learning by reinforcement can lead to probability matching and, if learning occurs suffciently slowly, probability matching does not only occur in choice frequencies but also in choice probabilities. Our results are completed by proving that there exists no quasi-linear reinforcement learning specification such that behavior is optimal for all environments where counterfactuals are observed.

Suggested Citation

  • Javier Rivas, 2011. "Probability Matching and Reinforcement Learning," Discussion Papers in Economics 11/20, Department of Economics, University of Leicester.
  • Handle: RePEc:lec:leecon:11/20
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    File URL: http://www.le.ac.uk/economics/research/repec/lec/leecon/dp11-20.pdf
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    References listed on IDEAS

    as
    1. 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 848-881, September.
    2. 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 921-950, November.
    3. Samuelson Larry, 1994. "Stochastic Stability in Games with Alternative Best Replies," Journal of Economic Theory, Elsevier, vol. 64(1), pages 35-65, October.
    4. Rubinstein, Ariel, 2002. "Irrational diversification in multiple decision problems," European Economic Review, Elsevier, vol. 46(8), pages 1369-1378, September.
    5. Kosfeld, Michael & Droste, Edward & Voorneveld, Mark, 2002. "A myopic adjustment process leading to best-reply matching," Games and Economic Behavior, Elsevier, vol. 40(2), pages 270-298, August.
    6. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
    7. Javier Rivas, 2008. "Learning within a Markovian Environment," Economics Working Papers ECO2008/13, European University Institute.
    8. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
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    More about this item

    Keywords

    Probability Matching; Reinforcement Learning;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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