COMMON PRIORS AND SEPARATION OF CONVEX-SETS

We observe that the set of all priors of an agent is the convex hull o f his types. A prior common to all agents exists if the sets of the ag ents' priors have a point in common, We give a necessary and sufficien t condition for the nonemptiness of the intersection of several closed convex subsets of the simplex, which is an extension of the separatio n theorem. A necessary and sufficient condition for the existence of c ommon prior is a special case of this. (C) 1998 Academic Press.