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Reinforcement Learning with Restrictions on the Action Set

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  • Mario Bravo

    ()
    (Instituto de Sistemas Complejos de Ingenieria (ISCI), Universidad de Chile)

  • Mathieu Faure

    ()
    (Aix-Marseille University (Aix-Marseille School of Economics), CNRS & EHESS)

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    Abstract

    Consider a 2-player normal-form game repeated over time. We introduce an adaptive learning procedure, where the players only observe their own realized payoff at each stage. We assume that agents do not know their own payoff function, and have no information on the other player. Furthermore, we assume that they have restrictions on their own action set such that, at each stage, their choice is limited to a subset of their action set. We prove that the empirical distributions of play converge to the set of Nash equilibria for zero-sum and potential games, and games where one player has two actions.

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    File URL: http://www.amse-aixmarseille.fr/sites/default/files/_dt/2012/wp_2013_-_nr_35.pdf#overlay-context=fr/recherche/documents-de-travail/reinforcement-learning-restrictions-action-set
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    Bibliographic Info

    Paper provided by Aix-Marseille School of Economics, Marseille, France in its series AMSE Working Papers with number 1335.

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    Length: 29 pages
    Date of creation: 01 Jul 2013
    Date of revision: 01 Jul 2013
    Handle: RePEc:aim:wpaimx:1335

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    Web page: http://www.amse-aixmarseille.fr/en
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    Related research

    Keywords: Reinforcement learning; fictitious play; Markovian procedures.;

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    1. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January.
    2. Ed Hopkins & Martin Posch, 2003. "Attainability of Boundary Points under Reinforcement Learning," Levine's Working Paper Archive 506439000000000350, David K. Levine.
    3. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
    4. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
    5. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
    6. Tilman B�rgers & Rajiv Sarin, . "Learning Through Reinforcement and Replicator Dynamics," ELSE working papers 051, ESRC Centre on Economics Learning and Social Evolution.
    7. Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
    8. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
    9. Berger, Ulrich, 2005. "Fictitious play in 2 x n games," Journal of Economic Theory, Elsevier, vol. 120(2), pages 139-154, February.
    10. Ed Hopkins, 2001. "Two Competing Models of How People Learn in Games," Levine's Working Paper Archive 625018000000000226, David K. Levine.
    11. 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 848-81, September.
    12. Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207.
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