A vector Lyapunov approach to the stability problem for the n-population continuous time replicator dynamics

Abstract

In this paper the stability problem for the n-population continuous time replicator dynamics using vector Lyapunov methods is addressed. After introducing the evolutionary stable strategy concept and proving that it is equivalent to being a strict Nash equilibrium, the n-population continuous time replicator dynamics equation is presented. Finally, it is shown that every strict Nash equilibrium is asymptotically stable in the associated dynamics via Lyapunov methods.