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thomblake comments on Prisoner's Dilemma Tournament Results - Less Wrong
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I thought of this too, but it really should play C then D to start so it cooperates against itself - otherwise, it will defect against itself.
Given the payoff matrix for this tournament, it isn't a very good strategy. However, if the payoff matrix rewarded D-C more strongly, then a pair of (tit-for-tat, tit-for-tat's complement) would do very well.