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Learning Through Reinforcement and Replicator Dynamics,☆☆

https://doi.org/10.1006/jeth.1997.2319Get rights and content

Abstract

This paper considers a version of R. R. Bush and F. Mosteller's (1951,Psych. Rev.58, 313–323; 1955, “Stochastic Models for Learning,” Wiley, New York) stochastic learning theory in the context of games. We show that in a continuous time limit the learning model converges to the replicator dynamics of evolutionary game theory. Thus we provide a non-biological interpretation of evolutionary game theory.Journal of Economic LiteratureClassification Numbers: C72, D83.

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    The material in this paper is taken from some sections of an earlier discussion paper of ours with the same title. We thank an associate editor, two referees, Murali Agastya, Ken Binmore, Vince Crawford, Drew Fudenberg, Nick Rau, Max Stinchcombe, and, especially, Joel Sobel for helpful comments and discussions. Part of this research was undertaken while Rajiv Sarin was visiting the Economics Department of University College London. He thanks the department for hospitality and financial support. Tilman Börgers thanks the Economic and Social Research Council for financial support under research Grant R000235526.

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    T. S. RobertsonH. H. Kassarjian, Eds.

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