In "Agreeing to Disagree" [1], Robert Aumann proves that a group of agents who once agreed about the probability of some proposition for which their current probabilities are common knowledge must still agree, even if those probabilities reflect disparate observations. Perhaps one saw that a card was red and another saw that it was a heart, so that as far as that goes, their common prior probability of 1/52 for its being the Queen of hearts would change in the one case to 1/26, and in the other to 1/13. But if those are indeed their current probabilities, it cannot be the case that both know them, and both know that both know them, etc., etc.