They may have other, differing information available to them, but the Aumann agreement process does not involve sharing such information.
What they do indirectly share is something like their confidence levels - and how much their confidence is shaken by the confidence of their partner in a different result.
Yes, Aumann agreement is not very realistic - but the point is that the partners can be expected to relatively quickly reach agreement, without very much effort - if they are honest, truth-seekers with some energy for educating others - and know the other is the same way.
So, the prevalance of persistent disagreements suggests that the world is not filled with honest, truth-seekers. Not very surprising, perhaps.
Yes, Aumann agreement is not very realistic - but the point is that the partners can be expected to relatively quickly reach agreement, without very much effort - if they are honest, truth-seekers with some energy for educating others - and know the other is the same way.
250 rounds of "I update my estimate to..." strikes me as rather a lot of effort, but that's not the important point here. My question is, assume that Alice and Bob are indeed honest truth-seekers with some energy for educating others, and have common knowledge that this is so....
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