"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.
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