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Notes -
Wouldn't it be outperformed by tit for tat with occasional unwarranted defection?
The specific case in which TfTwF outperforms TfT is a round-robin iterated prisoner's dilemma (scoring on total utility over all players/iterations) with many other players being TfT and a small amount of random noise added to people's decisions (i.e. "my hand slipped"). This is because, in this specific scenario, the random noise causes the TfT players to feud with each other quite extensively, whereas the feuds get cut short when there's a TfTwF involved and thus, while the TfT-vs.-TfTwF head-to-head is slightly in favour of TfT, TfTwF's self-play massively outperforms TfT's self-play.
If most players are not TfT (or very similar), TfT does better than TfTwF (as there either aren't any extensive feuds anyway, or the feuds - with e.g. Grim - can't be ended by forgiveness). If there is no noise, TfT does better than TfTwF.
TfT outperforms TfT-with-occasional-defection against TfTwF, unless the forgiveness time is too short*, as the feud, while relatively short, still outweighs the value of the defection.
*Obviously, the limit of TfTwF as forgiveness time goes to zero is just Co-operate-Bot, and we all know the optimal response to that is to spam defection.
Well, that changes the things rather significantly.
Come on, you've completely changed the meaning of the game at this point.
By "total utility" I meant "the total utility you score for yourself across all opponents". I will note that the object of PD is explicitly to score the most utility for yourself, not to outscore your opponent, so adding up the scores rather than counting "who scored more" matchups is more sensible.
I also think you might be misconstruing my intentions; what drove me to post was that @magicalkittycat misrepresented the game theory (there are a lot of people pushing that same line, so I'm not claiming malice) and I wanted to clarify it. I responded to you rather than to him because you asked a question about it which meant I wanted to alert you, the clarification and answer to the question didn't directly involve MKC so I wasn't required by honour to alert him (I am now), and MKC's kinda been on an angry rampage in this thread, including when replying to me, so I wasn't really feeling very enthused about the prospect of likely just getting a third earful for my trouble.
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