We consider a model of stochastic evolution under general noisy best response

protocols, allowing the probabilities of suboptimal choices to depend on their payoff

consequences. Our analysis focuses on behavior in the small noise double limit: we

first take the noise level in agents’ decisions to zero, and then take the population

size to infinity. We show that in this double limit, escape from and transitions between

equilibria can be described in terms of solutions to continuous optimal control

problems. These are used in turn to characterize the asymptotics of the the stationary

distribution, and so to determine the stochastically stable states. The control problems

are tractable in certain interesting cases, allowing analytical descriptions of the escape

dynamics and long run behavior of the stochastic evolutionary process.