The Common Prior Assumption (CPA) plays an important role in game theory and the economics of information. It is the basic assumption behind decision-theoretic justifications of equilibrium reasoning in games (Aumann, 1987, Aumann and Brandenburger, 1995) and no-trade results with asymmetric information (Milgrom and Stokey, 1982). Recently several authors (Dekel and Gul, 1997, Gul, 1996, Lipman, 1995) have questioned whether the CPA is meaningful in situations of incomplete information, where there is no ex ante stage and where the primitives of (...) the model are the individuals' beliefs about the external world (their first-order beliefs), their beliefs about the other individuals' beliefs (second-order beliefs), etc., i.e. their hierarchies of beliefs. In this context, the CPA is a mathematical property whose conceptual content is not clear. The main results of this paper (Theorems 1 and 2) provide a characterization of Harsanyi consistency in terms of properties of the belief hierarchies that are entirely unrelated to the idea of an ex ante stage. (shrink)

Given a finite state space and common priors, common knowledge of the identity of an agent with the minimal (or maximal) expectation of a random variable implies ‘consensus’, i.e., common knowledge of common expectations. This ‘extremist’ statistic induces consensus when repeatedly announced, and yet, with n agents, requires at most log2 n bits to broadcast.

Given common priors, no agent can publicly estimate a non-zero sign for the difference between his estimate and another agent’s future estimate. Thus rational agents cannot publicly anticipate the direction in which other agents will disagree with them.  2002 Elsevier Science B.V. All rights reserved.