Learning Strict Nash Equilibria through Reinforcement
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.
|Date of creation:||07 Oct 2011|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
Please 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.:
- Benaim, Michel & Weibull, Jörgen W., 2000.
"Deterministic Approximation of Stochastic Evolution in Games,"
Working Paper Series
534, Research Institute of Industrial Economics, revised 30 Oct 2001.
- Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, 05.
- K. Ritzberger & J. Weibull, 2010.
"Evolutionary Selection in Normal-Form Games,"
Levine's Working Paper Archive
452, David K. Levine.
- Vega-Redondo,Fernando, 2003.
"Economics and the Theory of Games,"
Cambridge University Press, number 9780521775908.
- Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
- Ed Hopkins & Martin Posch, 2003.
"Attainability of Boundary Points under Reinforcement Learning,"
ESE Discussion Papers
79, Edinburgh School of Economics, University of Edinburgh.
- Hopkins, Ed & Posch, Martin, 2005. "Attainability of boundary points under reinforcement learning," Games and Economic Behavior, Elsevier, vol. 53(1), pages 110-125, October.
- Ed Hopkins & Martin Posch, 2003. "Attainability of Boundary Points under Reinforcement Learning," Levine's Working Paper Archive 506439000000000350, David K. Levine.
- Alan Beggs, 2002.
"On the Convergence of Reinforcement Learning,"
Economics Series Working Papers
96, University of Oxford, Department of Economics.
- repec:oup:qjecon:v:87:y:1973:i:2:p:239-66 is not listed on IDEAS
- Borgers, Tilman & Sarin, Rajiv, 1997.
"Learning Through Reinforcement and Replicator Dynamics,"
Journal of Economic Theory,
Elsevier, vol. 77(1), pages 1-14, November.
- Tilman B�rgers & Rajiv Sarin, . "Learning Through Reinforcement and Replicator Dynamics," ELSE working papers 051, ESRC Centre on Economics Learning and Social Evolution.
- T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
- Izquierdo, Luis R. & Izquierdo, Segismundo S. & Gotts, Nicholas M. & Polhill, J. Gary, 2007. "Transient and asymptotic dynamics of reinforcement learning in games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 259-276, November.
- Arthur, W Brian, 1993. "On Designing Economic Agents That Behave Like Human Agents," Journal of Evolutionary Economics, Springer, vol. 3(1), pages 1-22, February.
- Ed Hopkins, 2001.
"Two Competing Models of How People Learn in Games,"
NajEcon Working Paper Reviews
- Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-81, September.
- Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
- Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:33936. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht)
If references are entirely missing, you can add them using this form.