Learning Strict Nash Equilibria through Reinforcement

Antonella Ianni

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Strict Nash Equilibrium; Reinforcement Learning (search for similar items in EconPapers)
JEL-codes: C72 C92 D83 (search for similar items in EconPapers)
Date: 2011-10-07
New Economics Papers: this item is included in nep-cis, nep-evo and nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Journal Article: Learning strict Nash equilibria through reinforcement (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:33936

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