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.
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- E. Dekel & S. Scotchmer, 2010.
"On the Evolution of Optimizing Behavior,"
Levine's Working Paper Archive
434, David K. Levine.
- 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.
- Ken Binmore & Larry Samuelson, 1994. "Muddling Through:Noisy Equilibrium Selection," Game Theory and Information 9403005, EconWPA, revised 29 Mar 1994.
- Ken Binmore & Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Game Theory and Information 9410002, EconWPA.
- Binmore, K. & Samuelson, L., 1994. "Muddling Through: Noisy Equilibrium selection," Working papers 9410, Wisconsin Madison - Social Systems.
- Schmalensee, Richard, 1975. "Alternative models of bandit selection," Journal of Economic Theory, Elsevier, vol. 10(3), pages 333-342, June.
- Ritzberger, Klaus & Weibull, Jörgen W., 1993.
"Evolutionary Selection in Normal Form Games,"
Working Paper Series
383, Research Institute of Industrial Economics.
- L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, 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.
- E. Akin & V. Losert, 2010. "Evolutionary Dynamics of zero-sum games," Levine's Working Paper Archive 424, David K. Levine.
- 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.
- 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.
- Samuelson, L. & Zhang, J., 1990.
"Evolutionary Stability In Symmetric Games,"
90-24, Wisconsin Madison - Social Systems.
- Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, 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.
- Itzhak Gilboa & Akihiko Matsui, 1992.
"A Model of Random Matching,"
- 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.
- 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.
- P. Taylor & L. Jonker, 2010. "Evolutionarily Stable Strategies and Game Dynamics," Levine's Working Paper Archive 457, David K. Levine.
- 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.
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