  We consider the Moran process with two populations competing under an
iterated Prisoners' Dilemma in the presence of mutation, and concentrate on the
case where there are multiple Evolutionarily Stable Strategies. We perform a
complete bifurcation analysis of the deterministic system which arises in the
infinite population size. We also study the Master equation and obtain
asymptotics for the invariant distribution and metastable switching times for
the stochastic process in the case of large but finite population. We also show
that the stochastic system has asymmetries in the form of a skew for parameter
values where the deterministic limit is symmetric.
