On imitation dynamics in potential population games

Imitation dynamics for population games are studied and their asymptotic properties analyzed. In the considered class of imitation dynamics — that encompass the replicator equation as well as other models previously considered in evolutionary biology — players have no global information about the game structure, and all they know is their own current utility and the one of fellow players contacted through pairwise interactions. For potential population games, global asymptotic stability of the set of Nash equilibria of the sub-game restricted to the support of the initial population configuration is proved. These results strengthen (from local to global asymptotic stability) existing ones and generalize them to a broader class of dynamics. The developed techniques highlight a certain structure of the problem and suggest possible generalizations from the fully mixed population case to imitation dynamics whereby agents interact on complex communication networks.