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 inter-acting 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. I