That is not the definition at the top of the paper you just linked for me: http://www.ma.huji.ac.il/~raumann/pdf/Agreeing%20to%20Disagree.pdf
"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."
Or I may have missed you point entirely. You have introduced the concept of "Aumann agreement exchange" but not what misconception you are trying to clear up with it.
Examples often help. I don't know if you have a misconception - but a common misconception is that A and B need to share their evidence pertaining to the temperature rise before they can reach agreement.
What Aumann says - counterintuitively - is that no, they just need to share their estimates of the temperature rise with each other repeatedly - so each can update on the other's updates - and that is all. As the Cowen quote from earlier says:
"In essence his opinion serves as a 'sufficient statistic' for all of his evidence".
-