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homunq comments on Prisoner's Dilemma Tournament Results - Less Wrong
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I don't care what my opponent will do this turn, I care how what they will do later depends on what I do now. That is, do they have the capacity to retaliate, or can I defect with impunity.
So basically, my strategy would be to see if they defect (or try to be sneaky by running out my cycles) on turn 100 if they think I'm a dumb TFT. If so, I attempt to defect 1 turn before they do (edit: or just TFT and plan to start defecting on turn 99), which becomes a battle to see whose recursion is more efficient. If not, I play TFT and we probably both cooperate all the way through, getting max stable points.
Significantly, my strategy would not do a last-turn defection against a dumb TFT, which leaves some points on the ground. However, it would try to defect against a (more TDT-like?) strategy which would defect against TFT; so if my strategy were dominant, it could not be attacked by a combination of TFT and some cleverer (TDT?) bot which defects last turn against TFT.
I call this strategy anti-omega, because it cooperates with dumb TFTs but inflicts some pain on Omegabot (the strategy which always gets the max points it could possibly get against any given opponent). Omegabot would still beat a combo of TFT and anti-omega (the extra points it would get from defecting last turn against TFT, and defecting turn 98 against anti-omega, would make up for the points it lost from having two mutual defections against anti-omega). But at least it would suffer for it.
This points to a case where TDT is not optimal decision theory: if non-TDT agents can reliably detect whether you are a "being too clever" (ie, a member of a class which includes TDT agents), and they punish you for it. Basically, no sense being a rationalist in the dark ages; even if you're Holmes or Moriarty, the chances that you'll slip up and be burned as a witch might outweigh the benefits.
I don't see rationality was a major cause of witch accusations. Indeed, a great number of successful dark agers seem to be ones that were cleverer / more rational than their contemporaries, even openly so.
Edited to show that I was trying to illustrate a concept concisely, not being historically accurate.