Narrow Results

The equilibrium selection model of Matsui and Matsuyama (1995), which is based on rational players who maximise their discounted future payoff, is analysed with the help of an associated differential game. Equilibrium selection results are derived for games with a ½-dominant equilibrium, for games with a potential function, and some simple supermodular games.

We give two generalizations of the Zhou fixed point theorem. They weaken the subcompleteness condition of values, and relax the ascending condition of the correspondence. As an application, we derive a generalization of Topkis’ theorem on the existence and order structure of the set of Nash equilibria of supermodular games.