Learning Strict Nash Equilibria through Reinforcement
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.Download Info
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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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Keywords:Other versions of this item:
- Ianni, Antonella, 2011. "Learning Strict Nash Equilibria through Reinforcement," MPRA Paper 33936, University Library of Munich, Germany.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-11-03 (All new papers)
- NEP-CBE-2007-11-03 (Cognitive & Behavioural Economics)
- NEP-GTH-2007-11-03 (Game Theory)
References
References listed on IDEASPlease report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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MPRA Paper
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Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Antonella Ianni, 2007.
"Learning Strict Nash Equilibria through Reinforcement,"
Economics Working Papers
ECO2007/21, European University Institute.
- Ianni, Antonella, 2011. "Learning Strict Nash Equilibria through Reinforcement," MPRA Paper 33936, University Library of Munich, Germany.
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