Limit sets of best-reply processes

Abstract

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.