The equilibrium selection approach of Matsui and Matsuyama (J. Econ. Theory
65 (1995), 415-434) 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 functi
on is the unique state that is absorbing and globally accessible for small
discount rates. (C) 1999 Academic Press.