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cousin_it comments on Agent-Simulates-Predictor Variant of the Prisoner's Dilemma - Less Wrong Discussion
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Yes, you can make the distinction mathematically precise, as I did in this post (which is the "Slepnev 2011" reference in the OP).
Yes, I understand that, but my question is why does the distinction matter in this context?
Not sure I understand your question... It's provable that the agents behave differently, so there you have a mathy explanation. As for non-mathy explanations, I think the best one is Gary's original description of the ASP problem.