Adjustment Dynamics and Rational Play in Games

When a strategic situation arises repeatedly, the possibility arises that equilibrium predictions can be justified by a dynamic adjustment process. We examine myopic adjustment dynamics, a class that includes replicator dynamics from evolutionary game theory, simple models of imitation, models of experimentation and adjustment, and some simple learning dynamics. We present a series of theorems showing conditions under which behavior that is asymptotically stable under some such dynamic is strategically stable (Kohlberg and Mertens [1986]). This behavior is thus as if the agents in the economy satisfied the extremely stringent assumptions that game theory traditionally makes about rationality and beliefs.