Fast convergence in evolutionary equilibrium selection

Stochastic best response models provide sharp predictions about equilibrium selection when the noise level is arbitrarily small. The difficulty is that, when the noise is extremely small, it can take an extremely long time for a large population to reach the stochastically stable equilibrium. An important exception arises when players interact locally in small close-knit groups; in this case convergence can be rapid for small noise and an arbitrarily large population. We show that a similar result holds when the population is fully mixed and there is no local interaction. Moreover, the expected waiting times are comparable to those in local interaction models. •We study an evolutionary model with noisy best response dynamics.•Agents interact globally and play a symmetric coordination game.•The dynamics exhibit fast convergence to the stochastically stable equilibrium.•Key factor: the noise level is not taken to zero.•Waiting times are small and comparable to those in local interaction models.