Learning Through Reinforcement and Replicator Dynamics
AbstractThis paper considers a version of Bush and Mosteller's stochastic learning theory in the context of games. We compare this model of learning to a model of biological evolution. The purpose is to investigate analogies between learning and evolution. We and that in the continuous time limit the biological model coincides with the deterministic, continuous time replicator process. We give conditions under which the same is true for the learning model. For the case that these conditions do not hold, we show that the replicator process continues to play an important role in characterising the continuous time limit of the learning model, but that a diï¿½erent eï¿½ect (\Probability Matching") enters as well.
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.
Bibliographic InfoPaper provided by David K. Levine in its series Levine's Working Paper Archive with number 380.
Date of creation: 08 Dec 2010
Date of revision:
Contact details of provider:
Web page: http://www.dklevine.com/
Other versions of this item:
- 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.
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-12-18 (All new papers)
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.:
- Boylan, Richard T., 1992. "Laws of large numbers for dynamical systems with randomly matched individuals," Journal of Economic Theory, Elsevier, vol. 57(2), pages 473-504, August.
- Samuelson, L. & Zhang, J., 1991.
"Evolutionary Stability in Asymmetric Games,"
9132, Tilburg - Center for Economic Research.
- E. Akin & V. Losert, 2010. "Evolutionary Dynamics of zero-sum games," Levine's Working Paper Archive 424, David K. Levine.
- Binmore, K. & Samuelson, L., 1994.
"Muddling Through: Noisy Equilibrium selection,"
9410, Wisconsin Madison - Social Systems.
- Ken Binmore & Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Game Theory and Information 9410002, EconWPA.
- Ken Binmore & Larry Samuelson, 1994. "Muddling Through:Noisy Equilibrium Selection," Game Theory and Information 9403005, EconWPA, revised 29 Mar 1994.
- Binmore, Ken & Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Discussion Paper Serie B 275, University of Bonn, Germany.
- Binmore, K. & samuelson, L., 1996. "Muddling Through : Noisy Equilibrium Section," Working papers 9410r, Wisconsin Madison - Social Systems.
- Mookherjee Dilip & Sopher Barry, 1994. "Learning Behavior in an Experimental Matching Pennies Game," Games and Economic Behavior, Elsevier, vol. 7(1), pages 62-91, July.
- Ritzberger, Klaus & Weibull, Jorgen W, 1995.
"Evolutionary Selection in Normal-Form Games,"
Econometric Society, vol. 63(6), pages 1371-99, November.
- E. Dekel & S. Scotchmer, 2010.
"On the Evolution of Optimizing Behavior,"
Levine's Working Paper Archive
434, David K. Levine.
- Cross, John G, 1973. "A Stochastic Learning Model of Economic Behavior," The Quarterly Journal of Economics, MIT Press, vol. 87(2), pages 239-66, May.
- Antonio Cabrales & Joel Sobel, 2010.
"On the Limit Points of Discrete Selection Dynamics,"
Levine's Working Paper Archive
432, David K. Levine.
- Cabrales, Antonio & Sobel, Joel, 1992. "On the limit points of discrete selection dynamics," Journal of Economic Theory, Elsevier, vol. 57(2), pages 407-419, August.
- P. Taylor & L. Jonker, 2010. "Evolutionarily Stable Strategies and Game Dynamics," Levine's Working Paper Archive 457, David K. Levine.
- Gilboa, Itzhak & Matsui, Akihiko, 1992.
"A model of random matching,"
Journal of Mathematical Economics,
Elsevier, vol. 21(2), pages 185-197.
- Schmalensee, Richard, 1975. "Alternative models of bandit selection," Journal of Economic Theory, Elsevier, vol. 10(3), pages 333-342, June.
- Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
- L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
- Antonio Cabrales, 1993.
"Stochastic replicator dynamics,"
Economics Working Papers
54, Department of Economics and Business, Universitat Pompeu Fabra.
- Boylan Richard T., 1995. "Continuous Approximation of Dynamical Systems with Randomly Matched Individuals," Journal of Economic Theory, Elsevier, vol. 66(2), pages 615-625, August.
- 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.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral 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: (David K. Levine).
If references are entirely missing, you can add them using this form.