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Well… if both are really “perfectly rational”, and they have common knowledge of each other’s rationality, then both should reason along the lines of “we’re both using the same decision algorithm. So our decisions are going to strongly correlate. So there’s effectively only two options: either both of us cooperate or booth of us defect. Both of us defecting sucks for me. Both of us cooperating isn’t too bad. So I should choose cooperate.”
Remember, “perfectly rational” people should generally do better than irrational people at stuff. Rationalists should win. So a pair of perfectly rational people should, when interacting, not screw themselves over simply because of their “rationality.” They should generally not ever have reason to regret their rationality.
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