The infinitely repeated Hell game having so many Nash equilibria really demonstrates how limited the concept of Nash equilibrium can be. How the hell would the strategy profile “Everyone plays 99, unless someone defects [by the way this could be by playing 30, an action which literally helps everyone], in which case we play 100” arise in the real world? The answer is… that’s a good question.
Indeed. Like, how could you know that other people are planning to respond to you playing 30 by “playing 100 until you go back to playing 99”? It’s unlikely that you, and many of the other players, would have found this out through experience, given that the strategy doesn’t dominate unless almost all the players are already playing it. And if there was a phase where players announced their strategies, why would this be the strategy they all announced? Seems to only be likely if the situation really is Hell, i.e. being ruled by a sadistic authoritarian who chose this strategy and forced everyone to agree to it (which raises a question of whether he’s still in control of the situation and how voluntary these choices are).
The most plausible real-world paths that come to mind are those in which the effects of people’s actions used to be completely different—where playing 99 was a good thing (because, I dunno, the place was initially freezing) (but I guess where 100 was a bad thing), so people did want to encourage everyone to play it, and that’s why they settled on the “play 99 or else be punished” strategy—and then it slowly morphed into the current situation, and I guess people were unable to communicate about it in the meantime.
Heavily-punished taboos, where you’re punished for even talking about, for actions that were believed to be bad in ancient times, but which e.g. science has shown to be harmless and beneficial today—that kind of thing would be potentially relevant. (Scott wrote a story that is somewhat related.)
Indeed. Like, how could you know that other people are planning to respond to you playing 30 by “playing 100 until you go back to playing 99”? It’s unlikely that you, and many of the other players, would have found this out through experience, given that the strategy doesn’t dominate unless almost all the players are already playing it. And if there was a phase where players announced their strategies, why would this be the strategy they all announced? Seems to only be likely if the situation really is Hell, i.e. being ruled by a sadistic authoritarian who chose this strategy and forced everyone to agree to it (which raises a question of whether he’s still in control of the situation and how voluntary these choices are).
The most plausible real-world paths that come to mind are those in which the effects of people’s actions used to be completely different—where playing 99 was a good thing (because, I dunno, the place was initially freezing) (but I guess where 100 was a bad thing), so people did want to encourage everyone to play it, and that’s why they settled on the “play 99 or else be punished” strategy—and then it slowly morphed into the current situation, and I guess people were unable to communicate about it in the meantime.
Heavily-punished taboos, where you’re punished for even talking about, for actions that were believed to be bad in ancient times, but which e.g. science has shown to be harmless and beneficial today—that kind of thing would be potentially relevant. (Scott wrote a story that is somewhat related.)