If you look at some of the neighboring text, I have some mathematical arguments about what the chances are for N people to all independently play “stag” such that no one plays rabbit and everyone gets the “stag reward”.
If 3 people flip coins, all three coins come up “stag” quite often. If a “stag” is worth roughly 8 times as much as a rabbit, you could still sanely “play stag hunt” with 2 other people whose skill at stag was “50% of the time they are perfect”.
But if they are less skilled than that, or there are more of them, the stag had better be very very very valuable.
If 1000 people flip coins then “pure stag” comes up one in every 9.33x10^302 times. Thus, de facto, stag hunts fail at large N except for one of those “dumb and dumber” kind of things where you hear the one possible coin pattern that gives the stag reward and treat this as good news and say “so you’re telling me there’s a chance!”
I think stag hunts are one of these places where the exact same formal mathematical model gives wildly different pragmatic results depending on N, and the probability of success, and the value of the stag… and you have to actually do the math, not rely on emotions and hunches to get the right result via the wisdom one one’s brainstem and subconscious and feelings and so on.
Coin flips are an absolutely inappropriate model for stag hunts; people choosing stag and rabbit are not independent in the way that coin flips are independent; that’s the whole point. Incentives drive everyone toward rabbit; agreements drive people toward stag. All of the reasoning descending from the choice to model things as coin flips is therefore useless.
If you look at some of the neighboring text, I have some mathematical arguments about what the chances are for N people to all independently play “stag” such that no one plays rabbit and everyone gets the “stag reward”.
If 3 people flip coins, all three coins come up “stag” quite often. If a “stag” is worth roughly 8 times as much as a rabbit, you could still sanely “play stag hunt” with 2 other people whose skill at stag was “50% of the time they are perfect”.
But if they are less skilled than that, or there are more of them, the stag had better be very very very valuable.
If 1000 people flip coins then “pure stag” comes up one in every 9.33x10^302 times. Thus, de facto, stag hunts fail at large N except for one of those “dumb and dumber” kind of things where you hear the one possible coin pattern that gives the stag reward and treat this as good news and say “so you’re telling me there’s a chance!”
I think stag hunts are one of these places where the exact same formal mathematical model gives wildly different pragmatic results depending on N, and the probability of success, and the value of the stag… and you have to actually do the math, not rely on emotions and hunches to get the right result via the wisdom one one’s brainstem and subconscious and feelings and so on.
Coin flips are an absolutely inappropriate model for stag hunts; people choosing stag and rabbit are not independent in the way that coin flips are independent; that’s the whole point. Incentives drive everyone toward rabbit; agreements drive people toward stag. All of the reasoning descending from the choice to model things as coin flips is therefore useless.