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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- 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., 1994. "Muddling Through: Noisy Equilibrium selection," Working papers 9410, Wisconsin Madison - Social Systems.
- Ken Binmore & Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Game Theory and Information 9410002, EconWPA.
- Binmore, K. & samuelson, L., 1996. "Muddling Through : Noisy Equilibrium Section," Working papers 9410r, Wisconsin Madison - Social Systems.
- Ritzberger, Klaus & Weibull, Jorgen W, 1995.
"Evolutionary Selection in Normal-Form Games,"
Econometric Society, vol. 63(6), pages 1371-99, November.
- Dekel, Eddie & Scotchmer, Suzanne, 1992.
"On the evolution of optimizing behavior,"
Journal of Economic Theory,
Elsevier, vol. 57(2), pages 392-406, August.
- Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
- 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.
- 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.
- Samuelson, L., 1989.
"Evolutionnary Stability In Asymmetric Games,"
11-8-2, Pennsylvania State - Department of Economics.
- Itzhak Gilboa & Akihiko Matsui, 1992.
"A Model of Random Matching,"
- Schmalensee, Richard, 1975. "Alternative models of bandit selection," Journal of Economic Theory, Elsevier, vol. 10(3), pages 333-342, June.
- Antonio Cabrales, 1993.
"Stochastic replicator dynamics,"
Economics Working Papers
54, Department of Economics and Business, Universitat Pompeu Fabra.
- P. Taylor & L. Jonker, 2010. "Evolutionarily Stable Strategies and Game Dynamics," Levine's Working Paper Archive 457, 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.
- 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.
- 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.
- L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
- 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.
- E. Akin & V. Losert, 2010. "Evolutionary Dynamics of zero-sum games," Levine's Working Paper Archive 424, David K. Levine.
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