Josef Hofbauer and Gerhard Sorger:

Perfect foresight and equilibrium selection in symmetric potential games

J. Economic Theory 85, 1-23 (1999).

Abstract. The equilibrium selection approach of Matsui and Matsuyama (JET) which is based on rational players who maximize their discounted future payoff, is analyzed for symmetric two-player games with a potential function. It is shown that the maximizer of the potential function is the unique state that is absorbing and globally accessible for small discount rates.

reprint


Josef Hofbauer and Gerhard Sorger, 2000:

A differential game approach to evolutionary equilibrium selection.

Int. Game Theory Review 4 (March 2002) 17-31.

Abstract. The equilibrium selection model of Matsui and Matsuyama (JET 1995), which is based on rational players who maximize their discounted future payoff, is analysed with the help of an associated differential game. Equilibrium selection results are derived for games with a 1/2-dominant equilibrium, for games with a potential function, and some simple supermodular games.
reprint


For further research in this direction see my page on Evolutionary equilibrium selection