Evolutionary drift and equilibrium selection

This paper develops an approach to equilibrium selection in game theory based on studying the learning process through which equilibrium is achieved. The differential equations derived from models of interactive learning typically have stationary states that are not isolated. Instead, Nash equilibria that specify different out-of-equilibrium behaviour appear in connected components of stationary states. The stability properties of these components can depend critically on the perturbations to which the system is subjected. We argue that it is then important to incorporate such drift into the model. A sufficient condition is provided for drift to create stationary states, with strong stability properties, near a component of equilibria. Applications to questions of forward and backward induction are developed.