I don’t really know about the theorem, but I think there’s something real here. I think the theorem is in spirit something like: “bad for everyone” equilibria can be enforced, as long as there’s a worse possible history. As long as there’s a worse possible history that can be enforced by everyone but you, regardless of what you do, then everyone but you can incentivize you to do any particular thing.
Like suppose you wake up and everyone tells you: we’ve all decided we’re going to torture everyone forever if you don’t pinch everyone you meet; but if you pinch everyone you meet, we won’t do that. So then your individually Nash-rational response is to pinch everyone you meet.
Ok so that gets one person. But this could apply to everyone. Suppose everyone woke up one day with some weird brain damage such that they have all the same values as before, except that they have a very specific and strong intention that if any single person fails to pinch everyone they meet, then everyone else will coordinate to torture everyone forever. Then everyone’s Nash-rational response is to pinch everyone.
But how can this be an equilibrium? Why wouldn’t everyone just decide to not do this torture thing? Isn’t that strictly better? If we’re just talking about Nash equilibria, the issue is that it counts as an equilibrium as long as what each player actually does is responding correctly given that everyone else’s policy is whatever it is. So even though it’s weird for players to harm everyone, it still counts as a Nash equilibrium, as long as everyone actually goes around pinching everyone in response. Pinch everyone is Nash-correct if everyone else would punish you, and indeed everyone else would punish you. Since everyone pinches everyone, no one has to actually torture everyone (which would be Nash-irrational, but that doesn’t matter).
But why would people have all this Nash-irrational behavior outside of what actually happens? It’s not actually necessary. https://en.wikipedia.org/wiki/Folk_theorem_(game_theory)#Subgame_perfection
You can apparently still get the result by, instead of “torture everyone forever” as the threat, have “torture everyone for a year” as the threat. Not sure exactly how this works, it seems to rely heavily on indifference?
Anyway, it’s also intuitively weird that people would have chosen some weird equilibrium like this in the first place. How do they suddenly leap to that equilibrium?
In real life a coalition doesn’t just punish defectors but also punishes people who don’t punish defectors, and so on. So to me it’s far from implausible that this would happen in real life.
I don’t really know about the theorem, but I think there’s something real here. I think the theorem is in spirit something like: “bad for everyone” equilibria can be enforced, as long as there’s a worse possible history. As long as there’s a worse possible history that can be enforced by everyone but you, regardless of what you do, then everyone but you can incentivize you to do any particular thing.
Like suppose you wake up and everyone tells you: we’ve all decided we’re going to torture everyone forever if you don’t pinch everyone you meet; but if you pinch everyone you meet, we won’t do that. So then your individually Nash-rational response is to pinch everyone you meet.
Ok so that gets one person. But this could apply to everyone. Suppose everyone woke up one day with some weird brain damage such that they have all the same values as before, except that they have a very specific and strong intention that if any single person fails to pinch everyone they meet, then everyone else will coordinate to torture everyone forever. Then everyone’s Nash-rational response is to pinch everyone.
But how can this be an equilibrium? Why wouldn’t everyone just decide to not do this torture thing? Isn’t that strictly better? If we’re just talking about Nash equilibria, the issue is that it counts as an equilibrium as long as what each player actually does is responding correctly given that everyone else’s policy is whatever it is. So even though it’s weird for players to harm everyone, it still counts as a Nash equilibrium, as long as everyone actually goes around pinching everyone in response. Pinch everyone is Nash-correct if everyone else would punish you, and indeed everyone else would punish you. Since everyone pinches everyone, no one has to actually torture everyone (which would be Nash-irrational, but that doesn’t matter).
But why would people have all this Nash-irrational behavior outside of what actually happens? It’s not actually necessary. https://en.wikipedia.org/wiki/Folk_theorem_(game_theory)#Subgame_perfection You can apparently still get the result by, instead of “torture everyone forever” as the threat, have “torture everyone for a year” as the threat. Not sure exactly how this works, it seems to rely heavily on indifference?
Anyway, it’s also intuitively weird that people would have chosen some weird equilibrium like this in the first place. How do they suddenly leap to that equilibrium?
In real life a coalition doesn’t just punish defectors but also punishes people who don’t punish defectors, and so on. So to me it’s far from implausible that this would happen in real life.