Large Games with Metrizable Characteristics∗

Abstract: In this paper we present a comprehensive analysis of large non-anonymous games in which the agents have a name as well as a type. The space of names is formu-lated as an abstract probability space while the space of types is a complete separable metric space. We show the existence of pure strategy Nash equilibria under alterna-tive cardinality assumptions on the common set of actions and on the space of types. When the action set is finite or countably infinite and compact, there exist pure strategy equilibria irrespective of any assumptions on the type space T. Two classes of results are presented on the atomless space of names: an abstract probability space or a Loeb probability space