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Learning Strict Nash Equilibria through Reinforcement

  • Ianni, Antonella

This paper studies the analytical properties of the reinforcement learning model proposed in Erev and Roth (1998), also termed cumulative reinforcement learning in Laslier et al (2001). This stochastic model of learning in games accounts for two main elements: the law of effect (positive reinforcement of actions that perform well) and the law of practice (the magnitude of the reinforcement effect decreases with players' experience). The main results of the paper show that, if the solution trajectories of the underlying replicator equation converge exponentially fast, then, with probability arbitrarily close to one, all the realizations of the reinforcement learning process will, from some time on, lie within an " band of that solution. The paper improves upon results currently available in the literature by showing that a reinforcement learning process that has been running for some time and is found suffciently close to a strict Nash equilibrium, will reach it with probability one.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 33936.

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Date of creation: 07 Oct 2011
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Handle: RePEc:pra:mprapa:33936
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  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 848-81, September.
  2. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
  3. Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207.
  4. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
  5. Vega-Redondo,Fernando, 2003. "Economics and the Theory of Games," Cambridge Books, Cambridge University Press, number 9780521775908, June.
  6. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
  7. Tilman Börgers & Rajiv Sarin, . "Learning Through Reinforcement and Replicator Dynamics," ELSE working papers 051, ESRC Centre on Economics Learning and Social Evolution.
  8. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
  9. Ed Hopkins & Martin Posch, 2003. "Attainability of Boundary Points under Reinforcement Learning," ESE Discussion Papers 79, Edinburgh School of Economics, University of Edinburgh.
  10. 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.
  11. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  12. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Gotts, Nicholas M. & Polhill, J. Gary, 2007. "Transient and asymptotic dynamics of reinforcement learning in games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 259-276, November.
  13. Benaim, Michel & Weibull, Jörgen W., 2000. "Deterministic Approximation of Stochastic Evolution in Games," Working Paper Series 534, Research Institute of Industrial Economics, revised 30 Oct 2001.
  14. Arthur, W Brian, 1993. "On Designing Economic Agents That Behave Like Human Agents," Journal of Evolutionary Economics, Springer, vol. 3(1), pages 1-22, February.
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