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. What then will the Aumann agreement process actually look like for this example, where the only thing that is directly communicated is each party's latest expectation of the value of the paper? Will it converge to the true value of the paper in both of the following scenarios:
No, I don't think it is true that both parties necessarily wind up with more accurate estimates after updating and agreeing, or even an estimate closer to what they would have obtained by sharing all their data.
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