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Learning within a Markovian Environment

Author

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  • Javier Rivas

Abstract

We investigate learning in a setting where each period a population has to choose between two actions and the payoff of each action is unknown by the players. The population learns according to reinforcement and the environment is non-stationary, meaning that there is correlation between the payoff of each action today and the payoff of each action in the past. We show that when players observe realized and foregone payoffs, a suboptimal mixed strategy is selected. On the other hand, when players only observe realized payoffs, a unique action, which is optimal if actions perform different enough, is selected in the long run. When looking for efficient reinforcement learning rules, we find that it is optimal to disregard the information from foregone payoffs and to learn as if only realized payoffs were observed.

Suggested Citation

  • Javier Rivas, 2008. "Learning within a Markovian Environment," Economics Working Papers ECO2008/13, European University Institute.
    • Handle: RePEc:eui:euiwps:eco2008/13
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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. Glenn Ellison & Drew Fudenberg, 1995. "Word-of-Mouth Communication and Social Learning," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(1), pages 93-125.
    3. John G. Cross, 1973. "A Stochastic Learning Model of Economic Behavior," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(2), pages 239-266.
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    Cited by:

    1. Yves Ortiz & Martin schüle, 2011. "Limited Rationality and Strategic Interaction: A Probabilistic Multi-Agent Model," Working Papers 11.08, Swiss National Bank, Study Center Gerzensee.
    2. Rivas, Javier, 2013. "Probability matching and reinforcement learning," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 17-21.

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    More about this item

    Keywords

    Adaptive Learning; Markov Chains; Non-stationarity; Reinforcement Learning;
    All these keywords.

    JEL classification:

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

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