Agreeing to Disagree
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.
Permanent link to this document: http://projecteuclid.org/euclid.aos/1176343654
Digital Object Identifier: doi:10.1214/aos/1176343654
Mathematical Reviews number (MathSciNet): MR433654
Zentralblatt MATH identifier: 0379.62003