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dankane comments on Robust Cooperation in the Prisoner's Dilemma - Less Wrong
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I have two proposed alternatives to PrudentBot.
If you can prove a contradiction, defect. Otherwise, if you can prove that your choice will be the same as the opponent's, cooperate. Otherwise, defect.
If you can prove that, if you cooperate, the other agent will cooperate, and you can't prove that if you defect, the other agent will cooperate, then cooperate. Otherwise, defect.
Both of these are unexploitable, cooperate with themselves, and defect against CooperateBot, if my calculations are correct. The first one is a simple way of "sanitizing" NaiveBot.
The second one is exactly cousin_it's proposal here.
Proposal 1 runs into the problem that it does not cooperate with itself if the two copies have slightly different bounds on proof lengths. Since if A cooperates, you can (with a not too long proof) show that B did not find a contradiction. But this contradicts the bounded version of the incompleteness theorem.
A similar problem holds for Proposal 2.
You can search for reasons to cooperate in a much stronger formal system than you search for reasons to defect in. Is there any decision-theoretic justification for this?
If you do that, you're back in the same situation that you started with and are cooperating with CooperateBot again.
This is clearly not true for proposal 2. No matter the formal system, you will find a proof (YouDefect => OpponentCooperate), and therefore defect.