An Approach to Equilibrium Selection

Abstract

We consider equilibrium selection in 2 × 2 bimatrix (both symmetric and asymetric) games with two strict Nash equilibria by embedding the static games in a dynamic random matching framework, played by a continuum of anonymous agents. Unlike in evolutionary games, the players are rational and maximize discounted payoffs, but they are restricted to make a short-run commitment when choosing actions. This dynamic game with frictions has stationary states, which correspond to the Nash equilibria of the static game. Our selection is based on differential stability properties of the stationary states. It is shown that, for a small degree of friction, a strict Nash equilibrium becomes uniquely absorbing (and globally accessible) if and only if it is risk-dominant (Harsanyi and Selten, "A General Theory of Equilibrium Selection in Games," MIT Press, Cambridge, MA, 1988). Journal of Economic Literature Classification Numbers: C72 and C73.