Fast Convergence in Evolutionary Equilibrium Selection

Stochastic learning models provide sharp predictions about equilibrium selection when the noise level of the learning process is taken to zero.  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.  Selection is sharp and convergence is fast when the noise level is 'fairly' small but not extremely small.