Waiting times in evolutionary dynamics with time-decreasing noise

Expected waiting times for equilibrium selection are exponentially increasing as the noise level goes to zero in evolutionary models with time‐constant noise, raising questions about whether the history independent prediction of equilibrium selection is relevant in economic and social studies. However, by using the theoretical results on simulated annealing, we show that expected waiting times in models with time‐decreasing noise need not tend toward infinity in the small noise limit. Our model thus describes conditions under which the waiting‐time critique of the predictions of stochastic stability theory may have less force.