Stochastic evolution with slow learning

Summary. This paper studies the extent to which diffusion approximations provide a reliable guide to equilibrium selection results in finite games. It is shown that they do for a class of finite games with weak learning provided that limits are taken in a certain order. The paper also shows that making mutation rates small does not in general select a unique equilibrium but making selection strong does. Received: January 19, 2000; revised version: September 25, 2000