Dynamic stability of the set of Nash equilibria in stable stochastic games

Evolutionary dynamics model the changes in state of a population and strategies used by individuals population. One gets different based on types dependence fitness or revision protocols. In this paper we define Perturbed Best Response (PBR), Brown-von Neumann-Nash (BNN), Replicator Projection for stochastic games, using framework evolutionary games. We also class stable discuss their properties, relations with constituent games game. Further, prove that set distributions inducing Nash equilibria is globally asymptotically BNN dynamics, while same shown case strictly PBR unique rest point perturbed equilibrium to be stable. These dynamic stability results are illustrated examples.