  We consider a broad class of stochastic imitation dynamics over networks,
encompassing several well known learning models such as the replicator
dynamics. In the considered models, players have no global information about
the game structure: they only know their own current utility and the one of
neighbor players contacted through pairwise interactions in a network. In
response to this information, players update their state according to some
stochastic rules. For potential population games and complete interaction
networks, we prove convergence and long-lasting permanence close to the
evolutionary stable strategies of the game. These results refine and extend the
ones known for deterministic imitation dynamics as they account for new
emerging behaviors including meta-stability of the equilibria. Finally, we
discuss extensions of our results beyond the fully mixed case, studying
imitation dynamics where agents interact on complex communication networks.
