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dclayh comments on The Aumann's agreement theorem game (guess 2/3 of the average) - Less Wrong
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Proposal for a variation: players may guess any positive real number, and the winner is the one closest to the first quartile of the distribution of answers. This removes both the anchoring effect of the upper bound and the effects of a few jokesters guessing Graham's number and Busybeaver(100) and so on.
It also has the feature of being somewhat more opaque to game-theoretic analysis, at least for me.
Graham's number isn't between 0 and 100.
Obviously. The change from 2/3 the mean to first quartile is only required because of the no-upper-bound change.