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Jack comments on Decision Theory Paradox: PD with Three Implies Chaos? - Less Wrong
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Um, they don't lose. What the TDT agents care about is the number of children they have. If they cared about the total number of descendants they have the cost of cooperating with DefectBots or CliqueBots would be exponentially higher (and TDT would act as CliqueBots).
Edit: Come to think of it, they wouldn't act like CliqueBots. Unlike CliqueBots they would also cooperate with CooperateBots. And if you include CooperateBots in the simulation TDT would beat CliqueBots.
Oh, good point. CliqueBot is a fail strategy! CliqueBot++ would need to allow exceptions such that it cooperates with (CliqueBoT++ && anything that it does not consider a serious rival).
TDT wouldn't cooperate with CooperateBot- that would be throwing away utility.
Er, it cooperates with two TDTs and one CooperateBot, it defects with two CooperateBots and one TDT. That TDT cooperates even when one of the other agents is a CooperateBot and not TDT gives it an edge over CliqueBot in a population that includes all three.
Sorry, I was thinking 2-player games. Your solution doesn't work, though; the CooperateBots vanish first, followed by the TDTs.
Maybe it wasn't clear: I'm proposing that if the TDT agents cared about their total descendants the strategy they would adopt would be the same as the CliqueBot except that they would cooperate with another TDT and a CooperateBot. Once the CooperateBots disappear TDT and CliqueBots would be using the same strategy except that there would be more TDTs (since they cooperated with the CooperateBots while they were around).
Ah! I hadn't thought of that wrinkle before- it makes my analogy (for next time) even stronger than I'd thought. Thanks!