Static and dynamic equilibria in games with continuum of players

This paper is a study of a general class of deterministic dynamic games with an atomless measure space of players and an arbitrary time space. The payoffs of the players depend on their own strategy, a trajectory of the system and a function with values being finite dimensional statistics of static profiles. The players' available decisions depend on trajectories of the system. The paper deals with relations between static and dynamic open-loop equilibria as well as their existence. An equivalence theorem is proven and theorems on the existence of a dynamic equilibrium are shown as consequences.