Ianni, Antonella (2011): Learning Strict Nash Equilibria through Reinforcement.

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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). 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.
Item Type:  MPRA Paper 

Original Title:  Learning Strict Nash Equilibria through Reinforcement 
Language:  English 
Keywords:  Strict Nash Equilibrium, Reinforcement Learning 
Subjects:  C  Mathematical and Quantitative Methods > C9  Design of Experiments > C92  Laboratory, Group Behavior D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D83  Search; Learning; Information and Knowledge; Communication; Belief C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  33936 
Depositing User:  Antonella Ianni 
Date Deposited:  07. Oct 2011 16:54 
Last Modified:  16. Feb 2013 05:28 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/33936 