An Approach to Equilibrium Selection

We consider equilibrium selection in 2x2 bimatrix games with two strict Nash equilibria in a random matching framework. The players seek to maximize the discounted payoffs, but are restricted to make a short run commitment. Modeling the friction this way yields equilibrium dynamics of the behavior patters in the society. We define and characterize an absorbing and globally attractive state in this dynamics. It is shown that, as friction becomes arbitrarily small, a strict Nash equilibrium outcome becomes unique absorbing and globally attractive if and only if it satisfies the Harsanyi/Selton notion of risk-dominance criterion.