Nash Certainty Equivalence in Large Population Stochastic Dynamic Games: Connections with the Physics of Interacting Particle Systems

Abstract

We consider large population dynamic games and illuminate methodological connections with the theory of interacting particle systems. Combined with the large population modelling, a Nash Certainty Equivalence (NCE) Methodology is introduced for specifying the localized strategy selection of a given agent within the Nash equilibrium setting. The NCE methodology closely parallels that found in the study of uncontrolled interacting particle systems within the framework of the McKean-Vlasov equation [19]: for both problems the solution is derived by focussing on a single generic individual at a microscopic level and analyzing its interaction with the ensemble of the other individuals of which it is itself, in a statistical sense, a representative.