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Best-Response Dynamics In A Birth-Death Model Of Evolution In Games



    (Department of Economics, University of Konstanz, Box 150, D-78457 Konstanz, Germany)



    (Socioeconomic Institute, University of Zurich, Hottingerstrasse 10 CH-8032 Zurich, Switzerland)

We consider a model of evolution with mutations as in Kandori et al. (1993) [Kandori, M., Mailath, G.J., Rob, R., 1993. Learning, mutation, and long run equilibria in games. Econometrica 61, 29–56], where agents follow best-response decision rules as in Sandholm (1998) [Sandholm, W., 1998. Simple and clever decision rules for a model of evolution. Economics Letters 61, 165–170]. Contrary to those papers, our model gives rise to a birth-death process, which allows explicit computation of the long-run probabilities of equilibria for given values of the mutation rate and the population size. We use this fact to provide a direct proof of the stochastic stability of risk-dominant equilibria as the mutation rate tends to zero, and illustrate the outcomes of the dynamics for positive mutation rates.

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Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 12 (2010)
Issue (Month): 02 ()
Pages: 197-204

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Handle: RePEc:wsi:igtrxx:v:12:y:2010:i:02:p:197-204
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