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

Carlos AlÓs-Ferrer, Ilja Neustadt

Research output: Contribution to journalArticlepeer-review

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

Original languageEnglish (US)
Pages (from-to)197-204
Number of pages8
JournalInternational Game Theory Review
Volume12
Issue number2
DOIs
StatePublished - Jun 2010

Keywords

  • Coordination games
  • birth-death processes
  • learning
  • mutation

ASJC Scopus subject areas

  • Computer Science(all)
  • Business and International Management
  • Statistics, Probability and Uncertainty

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