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Best-response dynamics in a birth-death model of evolution in games


Alós-Ferrer, Carlos; Neustadt, Ilja (2010). Best-response dynamics in a birth-death model of evolution in games. International Game Theory Review, 12(2):197-204.

Abstract

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 riskdominant equilibria as the mutation rate tends to zero, and illustrate the outcomes of the dynamics for positive mutation rates.

Abstract

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 riskdominant equilibria as the mutation rate tends to zero, and illustrate the outcomes of the dynamics for positive mutation rates.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Language:English
Date:June 2010
Deposited On:09 Jan 2011 09:09
Last Modified:06 Dec 2017 22:36
Publisher:World Scientific Publishing
ISSN:0219-1989
Publisher DOI:https://doi.org/10.1142/S021919891000260X

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