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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.

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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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  1. Ed Hopkins & Martin Posch, 2003. "Attainability of Boundary Points under Reinforcement Learning," Levine's Working Paper Archive 506439000000000350, David K. Levine.
  2. Michel Benaim & Mathieu Faure, 2010. "Stochastic Approximation, Cooperative Dynamics and Supermodular Games," Levine's Working Paper Archive 814577000000000437, David K. Levine.
  3. Drew Fudenberg & David Kreps, 2010. "Learning Mixed Equilibria," Levine's Working Paper Archive 415, David K. Levine.
  4. Ed Hopkins, 2001. "Two Competing Models of How People Learn in Games," Levine's Working Paper Archive 625018000000000226, David K. Levine.
  5. S. Hart & A. Mas-Collel, 2010. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Levine's Working Paper Archive 572, David K. Levine.
  6. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, June.
  7. Alan Beggs, 2002. "On the Convergence of Reinforcement Learning," Economics Series Working Papers 96, University of Oxford, Department of Economics.
  8. 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.
  9. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
  10. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May.
  11. 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.
  12. Berger, Ulrich, 2005. "Fictitious play in 2 x n games," Journal of Economic Theory, Elsevier, vol. 120(2), pages 139-154, February.
  13. 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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