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.
Length: Date of creation: 2007 Date of revision: 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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