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abramdemski comments on Aumann Agreement Game - Less Wrong Discussion
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Regardless of how well it follows the random walk, it already violates the assumption of rational agents.
Then why take Aumann's name in vain?
I think the relationship to Aumann's theorem is direct and strong. It's the same old question of how Aumann-like reasoning plays out in practice, for only partially rational agents, that was much discussed back in the Overcoming Bias days.
Probably the most relevant post:
http://www.overcomingbias.com/2007/01/we_cant_foresee.html
Another game proposed to shed light on this:
http://www.overcomingbias.com/2007/01/the_coin_guessi.html