We discuss two stochastic models of equilibrium selection in games
with two strict Nash equilibria. In the Kandori-Mailath-Rob model
(small matching noise) a risk-dominant equilibrium is stochastically stable.
In the Robson-Redondo model (large matching noise) a payoff-dominant
equilibrium is stochastically stable. We study the effect of the mutation level
and the number of players on equilibrium selection in the second model.
We show that for any arbitrarily low but fixed level of mutations,
if the number of players is sufficiently big, a risk-dominant equilibrium
is played in the long run with a frequency closed to one.
Key Words : evolutionary games, equilibrium selection, long-run behavior,
stochastic stability.