Time averages, recurrence and transience in the stochastic replicator dynamics

Abstract

We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that relates time averages of the process and Nash equilibria of a suitably modified game. Furthermore, a sufficient condition for transience is given in terms of mixed equilibria and definiteness of the payoff matrix. We also present necessary and sufficient conditions for stochastic stability of pure equilibria.

Published in at http://dx.doi.org/10.1214/08-AAP577 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• The long-run behavior of the stochastic replicator dynamics
• Generalized Urn Models of Evolutionary Processes

Cited by in corpus (4)

• The emergence of rational behavior in the presence of stochastic perturbations
• Unfair and Anomalous Evolutionary Dynamics from Fluctuating Payoffs
• A stochastic variant of replicator dynamics in zero-sum games and its invariant measures
• Widening Disparity and its Suppression in a Stochastic Replicator Model