Common priors and separation of convex sets

Abstract

We observe that the set of all priors of an agent is the convex hull of his types. A prior common to all agents exists if the sets of the agents' priors have a point in common. We give a necessary and sufficient condition for the nonemptiness of the intersection of several closed convex subsets of the simplex, which is an extension of the separation theorem. A necessary and sufficient condition for the existence of common prior is a special case of this. Journal of Economic Literature Classification Numbers: C70, D82. © 1998 Academic Press.