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Right, so we need to figure out what kinds of reasoning by symmetry are allowed under perfect rationality (in all possible games, not just this one). For exampl

Right, so we need to figure out what kinds of reasoning by symmetry are allowed under perfect rationality (in all possible games, not just this one). For example, should a rational person cooperate in the Prisoner's Dilemma because the opponent will be forced to cooperate by symmetry? In that case, won't irrational people eat rational people for breakfast, thus devaluing the idea that rational behavior maximizes utility? If you take the time to think it though, you might well reinvent superrationality, updateless decision theory and other fascinating things. In fact, you'll quickly get to questions that I have no idea how to solve!

darkmighty 11y ago
Yes I don't think this assumption makes a lot of sense in general if you don't assume your perfectly rational players have access to randomness (I do think it's the best assumption if the players can't communicate or have any entropy). In the case of Prisoner's Dilemma, if the cooperate/defect outcome had sufficiently large cooperation bonus for fixed other payoffs (large enough T>>R in wikipedia's notation), then with my assumptions it's clear that each prisoner should flip a coin to decide, and each one gets ~T/4 expected payoff. But the most glaring problem is of course assuming every player is perfectly rational. Personally I'd only assume that if your players are all game theorists with enough of time and paper :) I probably wouldn't even assume myself as rational. In conclusion, I believe equating maximin with optimal play/perfect rationality is misguided, but maximin is a good safe bet.
the_af 11y ago
What do you mean, "in all possible games"? The assumptions that hold for this game don't hold for the Prisoner's Dilemma. Like someone else said, you seem to be speaking in jargon. "Superrationality", "updateless decision theory", none of this matters in order to understand the Pirate Game. The rules of the game are very simple, maybe the pirates thing is throwing you off? That's just a theme for the puzzle (people aren't rational like this, and of course pirates aren't, and the whole situation is extremely artificial and unrealistic). The non-intuitive solution is derived from the rules as stated without any need for additional theory.

darkmighty 11y ago

Yes I don't think this assumption makes a lot of sense in general if you don't assume your perfectly rational players have access to randomness (I do think it's the best assumption if the players can't communicate or have any entropy). In the case of Prisoner's Dilemma, if the cooperate/defect outcome had sufficiently large cooperation bonus for fixed other payoffs (large enough T>>R in wikipedia's notation), then with my assumptions it's clear that each prisoner should flip a coin to decide, and each one gets ~T/4 expected payoff. But the most glaring problem is of course assuming every player is perfectly rational. Personally I'd only assume that if your players are all game theorists with enough of time and paper :) I probably wouldn't even assume myself as rational. In conclusion, I believe equating maximin with optimal play/perfect rationality is misguided, but maximin is a good safe bet.

the_af 11y ago

What do you mean, "in all possible games"? The assumptions that hold for this game don't hold for the Prisoner's Dilemma. Like someone else said, you seem to be speaking in jargon. "Superrationality", "updateless decision theory", none of this matters in order to understand the Pirate Game. The rules of the game are very simple, maybe the pirates thing is throwing you off? That's just a theme for the puzzle (people aren't rational like this, and of course pirates aren't, and the whole situation is extremely artificial and unrealistic). The non-intuitive solution is derived from the rules as stated without any need for additional theory.