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Learning Strict Nash Equilibria through Reinforcement

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Antonella Ianni

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Abstract

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). The stochastic model of learning accounts for two main elements: the Law of Effect (positive reinforcement of actions that perform well) and the Power Law of Practice (learning curves tend to be steeper initially). The paper establishes a relation between the learning process and the underlying deterministic replicator equation. The main results show that if the solution trajectories of the latter converge su¢ ciently fast, then the probability that all the realizations of the learning process over a given spell of time, possibly infinite, becomes arbitrarily close to one, from some time on. In particular, the paper shows that the property of fast convergence is always satisfied in proximity of a strict Nash equilibrium. The results also provide an explicit estimate of the approximation error that could prove to be useful in empirical analysis.

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Paper provided by European University Institute in its series Economics Working Papers with number ECO2007/21.

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Date of creation: 2007
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Handle: RePEc:eui:euiwps:eco2007/21

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information

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  1. Ianni, A., 2002. "Reinforcement Learning And The Power Law Of Practice: Some Analytical Results," Discussion Paper Series In Economics And Econometrics 0203, Economics Division, School of Social Sciences, University of Southampton.
  2. Ed Hopkins & Martin Posch, 2003. "Attainability of Boundary Points under Reinforcement Learning," Levine's Bibliography 506439000000000350, UCLA Department of Economics. [Downloadable!]
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  3. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November. [Downloadable!] (restricted)
  4. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November. [Downloadable!] (restricted)
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  5. Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207. [Downloadable!] (restricted)
  6. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  7. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
  8. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May. [Downloadable!] (restricted)
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