In this paper we model an evolutionary process with perpetual random shocks, where individuals sample population-specific strategy and payoff realizations and imitate the most successful behavior. For finite n-player games we prove that in the limit, as the perturbations tend to zero, only...

This paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games. The deterministic approximation is defined in continuous time as a system of ordinary differential equations of the type studied in evolutionary game...