Dov Samet (Faculty of Management Tel Aviv University)
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 non-emptiness 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.
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