An Approach to Equilibrium Selection

We consider equilibrium selection in 2x2 bimatrix (both symmetric and asymmetric) games with two strict Nash equilibria by embedding it in a dynamic random matching game played by a continuum of anonymous agents. Unlike in the evolutionary game literature, we assume that the players are rational, seeking to maximize the expected discounted payoffs; but they are instead restricted to make a short run commitment when choosing actions. Modeling the friction this way yields the equilibrium dynamics, whose stationary states correspond to the Nash outcomes of the original game. Our selection is based on differential stability properties of the stationary states. It is shown that, as friction becomes arbitrarily small, a strict Nash outcome becomes uniquely absorbing and globally accessible if and only if it satisfies the Harsanyi and Selton (1988) notion of risk-dominance criterion. Our approach thus supplies another support for risk-dominance in addition to those given in literature.