I analyze limiting behavior of best-reply processes. I find that without inertia
Nash Equilibria are not limit sets. Moreover, even for processes with inertia,
Nash Equilibria are not stable.
I argue that minimal CURB sets are reasonable candidates for limit sets if
best-reply processes are indeterminate or Nash Equilibria satisfy evolutionary
stability (Oechssler 1997). In such cases, limit sets necessarily contain a Nash
Equilibrium. Otherwise limit sets may not be close to any Nash Equilibria
unless they satisfy some support consistency condition.