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Vladimir_Nesov comments on The Aumann's agreement theorem game (guess 2/3 of the average) - Less Wrong
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Comments (149)
Conspiracy is a strategy that leads to winning, while "defecting" is something magical, a change that doesn't exist in isolation. If it was possible for one player to jump to a winning position, while other players remain where they were, then this is obviously preferable to that player, but that's not really the case.
Adhering to the conspiracy is a strategy that leads to losing if anyone else answers slightly below 100. It's not a strategy that exists in isolation either.
ETA: More generally, if you're going to try to undermine a basic concept in game theory as being "magical" (whatever that is supposed to mean), I think you owe more of an argument than the one you've given.
Vladimir is just following the footsteps of Aumann, who in 1959 proposed the notion of Strong Nash Equilibrium, which requires that an agreement not be subject to an improving deviation by any coalition of players. Other game theorists then realized (like conchis) that this requirement is too strong, since agreements must be resistant to deviations which are not themselves resistant to further deviations. (I'm mostly quoting from http://www.u.arizona.edu/~jwooders/cpcethry.pdf here.)
I propose that nobody should be downvoted for making a mistake that Aumann made. :)
What about mistakes that he continues to make? ;)
More generally, although I didn't vote Vladimir down (I have a general policy against voting down comments in conversations I'm actively involved in) I'm perfectly happy to vote down mistakes regardless of whether someone smart has made them before.