The Nash certainty equivalence principle and McKean-Vlasov systems: An invariance principle and entry adaptation

We study large population stochastic dynamic games where the so-called Nash certainty equivalence based control laws are implemented by the individual players. We first show a martingale property for the limiting control problem of a single agent and then perform averaging across the population; this procedure leads to a constant value for the martingale which shows an invariance property of the population behavior induced by the Nash strategies. The situation of a new agent joining the population is also analyzed.