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John_Maxwell_IV comments on The Aumann's agreement theorem game (guess 2/3 of the average) - Less Wrong
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There's no reason for the game to go all the way down to 0. If everyone is playing 1, that's an equilibrium because 2/3 of 1 is closer to 1 than 0.
That's not a Nash equilibrium.
Are players allowed to guess non-integers? Edit: Warrigal says they are. I'm wrong, you're right.