IDEAS home Printed from
   My bibliography  Save this paper

Learning within a Markovian Environment


  • Javier Rivas


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

    Download full text from publisher

    File URL:
    File Function: main text
    Download Restriction: no

    References listed on IDEAS

    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, Oxford University Press, vol. 110(1), pages 93-125.
    3. John G. Cross, 1973. "A Stochastic Learning Model of Economic Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 87(2), pages 239-266.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Rivas, Javier, 2013. "Probability matching and reinforcement learning," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 17-21.
    2. 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.

    More about this item


    Adaptive Learning; Markov Chains; Non-stationarity; Reinforcement Learning;

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eui:euiwps:eco2008/13. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Julia Valerio). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.