On imitation dynamics in potential population games

TL;DR

This paper analyzes imitation dynamics in potential population games, proving global stability of Nash equilibria and extending previous results to broader classes of dynamics and interaction networks.

Contribution

It generalizes stability results for imitation dynamics in potential population games, moving from local to global stability and considering complex interaction networks.

Findings

Global asymptotic stability of Nash equilibria established

Results extend to broader classes of imitation dynamics

Techniques suggest applicability to complex communication networks

Abstract

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.