BEST-RESPONSE DYNAMICS IN A BIRTH-DEATH MODEL OF EVOLUTION IN GAMES

Carlos Alós-Ferrer and Ilja Neustadt

International Game Theory Review (IGTR), 2010, vol. 12, issue 02, 197-204

Abstract: We consider a model of evolution with mutations as in Kandoriet 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.

Keywords: Coordination games; learning; mutation; birth-death processes; C72; D83 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S021919891000260X

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