On abstract economies with an arbitrary set of players and action sets in locally-convex topological vector spaces

In this paper we show the existence of equilibrium in an abstract economy with an arbitrary set of players, each of whose compact convex action sets lie in different locally convex spaces, and whose preferences obey weaker continuity postulates that have been used in the original treatments of Arrow and Debreu in the early fifties, and of Shafer and Sonnenschein in the mid-seventies. Our theorem synthesizes results around the cardinality of the set of agents, and incorporates in particular recent results of Carmona–Podczeck and He–Yannelis. The proof of the theorem is based on nonstandard analysis and its novelty has independent methodological interest.