Evolutionary Dynamics with Aggregate Shocks
Abstract We study the evolution of the continuous-time replicator dynamics when payoffs are subject to aggregate shocks that take the form of a Wiener process. In the absence of “mutation”, the system need not have an ergodic distribution. With mutation, the system does have an ergodic distribution. In the limit as the mutation rate and the variance of the shocks converge to zero, this distribution concentrates on the risk-dominant equilibrium. This result is not, however, robust to changes in the underlying deterministic dynamics.