Learning Through Reinforcement and Replicator Dynamics
This 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 di®erent e®ect (\Probability Matching") enters as well.
(This abstract was borrowed from another version of this item.)
If 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.
References listed on IDEAS
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.:
- Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
- Dekel, Eddie & Scotchmer, Suzanne, 1992.
"On the evolution of optimizing behavior,"
Journal of Economic Theory,
Elsevier, vol. 57(2), pages 392-406, August.
- Cabrales, Antonio, 2000.
"Stochastic Replicator Dynamics,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(2), pages 451-81, May.
- 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.
- Gilboa, Itzhak & Matsui, Akihiko, 1992.
"A model of random matching,"
Journal of Mathematical Economics,
Elsevier, vol. 21(2), pages 185-197.
- Binmore, K. & Samuelson, L., 1994.
"Muddling Through: Noisy Equilibrium selection,"
9410, Wisconsin Madison - Social Systems.
- Binmore, K. & samuelson, L., 1996. "Muddling Through : Noisy Equilibrium Section," Working papers 9410r, Wisconsin Madison - Social Systems.
- Binmore, Ken & Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Discussion Paper Serie B 275, University of Bonn, Germany.
- 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.
- K. Ritzberger & J. Weibull, 2010.
"Evolutionary Selection in Normal-Form Games,"
Levine's Working Paper Archive
452, David K. Levine.
- 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.
- 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.
- Samuelson, L., 1989.
"Evolutionnary Stability In Asymmetric Games,"
11-8-2, Pennsylvania State - Department of Economics.
- P. Taylor & L. Jonker, 2010. "Evolutionarily Stable Strategies and Game Dynamics," Levine's Working Paper Archive 457, David K. Levine.
- 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.
- John G. Cross, 1973. "A Stochastic Learning Model of Economic Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 87(2), pages 239-266.
- 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.
- E. Akin & V. Losert, 2010. "Evolutionary Dynamics of zero-sum games," Levine's Working Paper Archive 424, David K. Levine.
- L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
- Schmalensee, Richard, 1975. "Alternative models of bandit selection," Journal of Economic Theory, Elsevier, vol. 10(3), pages 333-342, June.
When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:77:y:1997:i:1:p:1-14. 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: (Shamier, Wendy)
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.