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Reinforcement Learning with Restrictions on the Action Set


  • Mario Bravo

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

  • Mathieu Faure

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


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.

Suggested Citation

  • Mario Bravo & Mathieu Faure, 2013. "Reinforcement Learning with Restrictions on the Action Set," AMSE Working Papers 1335, Aix-Marseille School of Economics, Marseille, France, revised 01 Jul 2013.
  • Handle: RePEc:aim:wpaimx:1335

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    References listed on IDEAS

    1. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
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    7. Michel Benaim & Mathieu Faure, 2010. "Stochastic Approximation, Cooperative Dynamics and Supermodular Games," Levine's Working Paper Archive 814577000000000437, David K. Levine.
    8. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
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    10. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
    11. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, January.
    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.
    13. 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.
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    Reinforcement learning; fictitious play; Markovian procedures.;

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