Perfectly updating on the basis of others' opinions is rare; I have never seen anyone who purports to do it correctly (I can't update correctly on the basis of almost anything). Common knowledge of this ability seems impossible to come by. Common knowledge that neither of you is trying to manipulate the other (or speaking for signaling reasons) is also completely non-existent: I have never been in an environment where more than 2 or 3 levels of non-manipulation were known.