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conchis comments on The Aumann's agreement theorem game (guess 2/3 of the average) - Less Wrong
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Comments (149)
It's the only Nash equilibrium. The only way everyone can win (and thus, the only way no-one would want to change their guess if they knew all the other guesses) is for all of us to guess a number that is 2/3 of itself: i.e. 0.
ETA: CannibalSmith's explanation is better.
ETA2: AllanCrossman's is even better.
Then I don't see the point of the game.
For this to apply in the real world, the players not only have to be rational, they also have to have common knowledge of each others' rationality. E.g. even if you're rational, if you think I'm stupid, and will guess 5, then you should no longer guess zero. Even if I am rational, and everyone else has common knowledge of everyone else's rationality, if they know that you think I'm irrational, then they know that you'll guess higher than zero, so they'll all guess higher than zero, and so on...
In general, the more "stupid" people there are, or the more "stupid" people we think there are, or the more "stupid" people we think others think there are, or... the further the average guess is likely to be from 0. So (I assume) the point is to test the assumption of common knowledge of rationality: i.e. how stupid people are, how stupid we think other people are, how stupid we think other people think other people are, etc.