Commonality of information and commonality of beliefs
2025-11-17
A group of agents with a common prior receive informative signals about an unknown state repeatedly over time. If these signals were public, agents' beliefs would be identical and commonly known. This suggests that if signals were private, then the more correlated they are, the greater is the commonality of beliefs. We show that, in fact, the opposite may be true. In the long run, conditionally independent signals may achieve greater commonality of beliefs than correlated signals.