Adjustment Dynamics and Rational Play in Games

When a given 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 asymptomatically stable under some such dynamic is strategically stable in the sense of Kohlberg and Mertens. This behavior is this as is the agents in the economy satisfied the extremely stringent assumptions that game theory traditionally makes about rationality and beliefs.