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shinoteki comments on Robust Cooperation in the Prisoner's Dilemma - Less Wrong
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Should this be "If you can prove that you will cooperate, defect"? As it is, I don't see how this prevents cooperation with Cooperatebot, unless the agent uses an inconsistent system for proofs.
It kills the Lobian argument, I believe, since this implication "if there's a proof that you cooperate, then cooperate " is no longer true. Instead, here's a Lobian argument for defection:
Suppose there is a proof that you defect. Then either there is a proof of contradiction, or there is no proof that your move is the same as your opponent's. Either way, you defect.