Two people, 1 and 2, are said to have common knowledge of an event $E$ if both know it, 1 knows that 2 knows it, 2 knows that 1 knows is, 1 knows that 2 knows that 1 knows it, and so on. THEOREM. If two people have the same priors, and their posteriors for an event $A$ are common knowledge, then these posteriors are equal.
"Agreeing to Disagree." Ann. Statist. 4 (6) 1236 - 1239, November, 1976. https://doi.org/10.1214/aos/1176343654