A note on adjusted replicator dynamics in iterated games
AbstractWe establish how a rich collection of evolutionary games can arise as asymptotically exact descriptions of player strategies in iterated games. We consider arbitrary normal-form games that are iteratively played by players that observe their own payoffs after each round. Each player's strategy is assumed to depend only past actions and past payoffs of the player. We study a class of autonomous reinforcement-learning rules for such players and show that variants of the adjusted replicator dynamics are asymptotically exact approximations of player strategies for small values of a step-size parameter adopted in learning. We also obtain a convergence result that identifies when a stable equilibrium of the limit dynamics characterizes equilibrium behavior of player strategies.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 46 (2010)
Issue (Month): 1 (January)
Contact details of provider:
Web page: http://www.elsevier.com/locate/jmateco
Adjusted replicator dynamics Reinforcement learning Stochastic approximations;
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.:
- Beggs, A.W., 2005.
"On the convergence of reinforcement learning,"
Journal of Economic Theory,
Elsevier, vol. 122(1), pages 1-36, May.
- 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.
- Tilman B�rgers & Rajiv Sarin, .
"Learning Through Reinforcement and Replicator Dynamics,"
ELSE working papers
051, ESRC Centre on Economics Learning and Social Evolution.
- Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
- T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
- K. Schlag, 2010.
"Why Imitate, and if so, How? Exploring a Model of Social Evolution,"
Levine's Working Paper Archive
454, David K. Levine.
- Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
- Hofbauer, Josef & Karl H. Schlag, .
"Sophisticated Imitation in Cyclic Games,"
Discussion Paper Serie B
427, University of Bonn, Germany, revised Mar 1998.
- Borgers, Tilman & Sarin, Rajiv, 2000.
"Naive Reinforcement Learning with Endogenous Aspirations,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 921-50, November.
- Tilman B�rgers & Rajiv Sarin, . "Naive Reinforcement Learning With Endogenous Aspiration," ELSE working papers 037, ESRC Centre on Economics Learning and Social Evolution.
- T. Borgers & R. Sarin, 2010. "Naïve Reinforcement Learning With Endogenous Aspirations," Levine's Working Paper Archive 381, David K. Levine.
- DellaVigna, Stefano & LiCalzi, Marco, 2001. "Learning to make risk neutral choices in a symmetric world," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 19-37, January.
- J.-F. Laslier & R. Topol & B. Walliser, 1999.
"A behavioral learning process in games,"
THEMA Working Papers
99-03, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- 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.
- Karl H. Schlag, 1995.
"Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits,"
Discussion Paper Serie B
361, University of Bonn, Germany, revised Mar 1996.
- Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
- Karl H. Schlag, . "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers 028, ESRC Centre on Economics Learning and Social Evolution.
- Ed Hopkins, 2001.
"Two Competing Models of How People Learn in Games,"
NajEcon Working Paper Reviews
- Sarin, Rajiv & Vahid, Farshid, 1999. "Payoff Assessments without Probabilities: A Simple Dynamic Model of Choice," Games and Economic Behavior, Elsevier, vol. 28(2), pages 294-309, August.
- Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207.
- R. Boylan, 2010. "Continuous Approximation of Dynamical Systems with Randomly Matched Individuals," Levine's Working Paper Archive 372, David K. Levine.
- Corradi, Valentina & Sarin, Rajiv, 2000. "Continuous Approximations of Stochastic Evolutionary Game Dynamics," Journal of Economic Theory, Elsevier, vol. 94(2), pages 163-191, October.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.