The problem (with the edited scenario) is that, without an enforcement mechanism, all the players in the conspiracy have an incentive to defect (more precisely, they’re indifferent between defecting and not defecting if they don’t care how many winners there are; they strictly prefer defection if they would rather be the only winner.)
Fun fact: a similar conspiracy strategy won the 20th anniversary iterated Prisoner’s Dilemma tournament, beating out Tit For Tat.
Your words hint that, if adherence to Aumann’s theorem is to be considered the measure of a rationalist, then invariably defecting in PD and conspiracy situations should be regarded as an equally valid measure. But then we’d have to drop Eliezer from the ship.
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. :)
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.
The problem (with the edited scenario) is that, without an enforcement mechanism, all the players in the conspiracy have an incentive to defect (more precisely, they’re indifferent between defecting and not defecting if they don’t care how many winners there are; they strictly prefer defection if they would rather be the only winner.)
Fun fact: a similar conspiracy strategy won the 20th anniversary iterated Prisoner’s Dilemma tournament, beating out Tit For Tat.
Your words hint that, if adherence to Aumann’s theorem is to be considered the measure of a rationalist, then invariably defecting in PD and conspiracy situations should be regarded as an equally valid measure. But then we’d have to drop Eliezer from the ship.
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.