I characterize the implications of the common prior assumption for finite orders of beliefs about beliefs at a state and show that the only such implications are those stemming from the weaker assumption of a common support. More precisely, given any model where priors have the same support and...

We have found several propositions in the economics of information which depend on the log of the cumulative distribution distribution of a random variable being a concave function. In this paper we present several theorems and applications of the property of log-concavity.