This article considers the robustness of long run equilibria when muta
tion rates are not assumed to be constant over time. Particular attent
ion is paid to the case where mutation rates decline to zero in the li
mit. It is Found that if behavior is ergodic, then it corresponds to t
he long run equilibrium for the game. However, conditions for ergodici
ty become increasingly restrictive as population size increases. (C) 1
998 Academic Press.