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cousin_it comments on The Aumann's agreement theorem game (guess 2/3 of the average) - Less Wrong
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Good, but it's even more interesting.
a) I have successfully moved the average by ~2X compared to if I'd stayed silent.
b) If N is known and everyone acts rationally as you describe, a pair of colluding players can screw everyone over: one guesses 100, the other guesses the new average.
The combined effect is making my brain explode.
If I may attempt to contribute your brain matter's outward velocity: When I was contemplating submitting a guess (which I didn't do), I actually concluded (I have no evidence for this, sorry) that you in particular would probably guess 100. Had I acted on that, the effect would have been nearly the same, except for the possibility that others would be drawing the same inference.