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orthonormal comments on Robust Cooperation in the Prisoner's Dilemma - Less Wrong
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If I were submitting a modal agent, I'd probably use a PrudentBot that uses PA to look for mutual cooperation but PA+N (for some large N) to look for defection against DefectBot. There's not a simple downside to that variant.
In particular, Prudent(0,100)Bot finds mutual cooperation with Prudent(0,1)Bot, Prudent(99,1000)Bot, etc.
Or breakout the stronger systems, e.g., ZFC possibly with some inaccessible cardinals thrown in for good measure.
That would be even better in practice, but it wouldn't be expressible in the modal formalism.