Quantal response methods for equilibrium selection in 2 × 2 coordination games

The notion of quantal response equilibrium (QRE), introduced by McKelvey and Palfrey (1995), has been widely used to explain experimental data. In this paper, we use quantal response equilibrium as a homotopy method for equilibrium selection, and study this in detail for 2×2 bimatrix coordination games. We show that the risk dominant equilibrium need not be selected. In the logarithmic game, the limiting QRE is the Nash equilibrium with the larger sum of square root payoffs. Finally, we apply the quantal response methods to the mini public goods game with punishment. A cooperative equilibrium can be selected if punishment is strong enough.