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orthonormal comments on Robust Cooperation in the Prisoner's Dilemma - Less Wrong
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Here is another obstacle to an optimality result: define UnfairBot as the agent which cooperate with X if and only if PA prove that X defect against UnfairBot, then no modal agent can get both FairBot and UnfairBot to cooperate with it.
Right! More generally, I claim that if a modal agent provably cooperates (in PA) against some other agent, then it cannot provably defect (in PA) against any other agent: roughly speaking, PA can never prove that any proof search in PA or higher fails, so a modal agent can only provably (in PA) do the action that it would do if PA were inconsistent.