  This paper compares two learning processes, namely those generated by
replicator and best-response dynamics, from the point of view of the
asymptotics of play. We base our study on the intersection of the basins of
attraction of locally stable pure Nash equilibria for replicator and
best-response dynamics. Local stability implies that the basin of attraction
has positive measure but there are examples where the intersection of the basin
of attraction for replicator and best-response dynamics is arbitrarily small.
We provide conditions, involving the existence of an unstable interior Nash
equilibrium, for the basins of attraction of any locally stable pure Nash
equilibrium under replicator and best-response dynamics to intersect in a set
of positive measure. Hence, for any choice of initial conditions in sets of
positive measure, if a pure Nash equilibrium is locally stable, the outcome of
learning under either procedure coincides. We provide examples illustrating the
above, including some for which the basins of attraction exactly coincide for
both learning dynamics. We explore the role that indifference sets play in the
coincidence of the basins of attraction of the stable Nash equilibria.
