You argue that TFT-n, for some n is then invaded by TFT, so there is a “rock, scissors, paper” cycle, but how does that work? A solitary TFT will co-operate one more time than the surrounding population of TFT-n, and will meet defection in that final co-operation so it has a strictly lower fitness than TFT-n. So it can’t invade.
Oops, you’re right- there’s a minimum “foothold” proportion (depending on the payoffs and on n) that’s required. But if foothold-sized cliques of various TFT-n agents are periodically added (i.e. random mutations), then you get that cycle again—and in the right part of the cycle, it is individually beneficial to be TFT rather than TFT-n, since TFT-n never gets cooperation on any of the last (n-1) turns.
On your other point, it’s worth noting that organisms are adaptation-executors, not fitness-maximizers; it seems easier to evolve generally altruistic values (combined with a memory of past defectors to avoid getting exploited by them or by similar agents again) than to evolve a full calculator for when defection would be truly without cost.
This “clique” solution has some problems. First, a single mutant can’t form a clique. OK, but maybe the mutant is interacting with nearby individuals, some of whom also share the mutation? That works if the nearby partners are relatives, but the difficulty there is that kin selection would already be favouring co-operation with neighbours, so how does TFT get an advantage? You can juggle with the pay-offs and the “shadow of the future” probability to try and get this to work (i.e. find a set of parameters where co-operation with neighbours via kin selection is not favoured, whereas TFT is), but it all looks a bit shaky.
Andreas Griger below suggests that the TFT mutants preferentially interact with each other rather than the TFT-n (or DefectBots) around them. This is another solution, though it adds to the overhead/complexity of a successful invader. However, it does lead to a nice testable prediction: species which practice reciprocation with non-relatives will also practice partner selection.
The point about adaptation executors not being fitness maximizers was also brought up by Unnamed below though see my response. The general issue is that citing the link is not an all-purpose excuse for maladaptation (what Richard Dawkins once referred to as the “evolution has bungled again” explanation). In particular you might want to see a paper by Fehr and Henrich Is Strong Reciprocity a maladaptation? which looks at the maladaptation hypothesis in detail and shows that it just doesn’t fit the evidence. Definitely worth a read if you have time.
Oops, you’re right- there’s a minimum “foothold” proportion (depending on the payoffs and on n) that’s required. But if foothold-sized cliques of various TFT-n agents are periodically added (i.e. random mutations), then you get that cycle again—and in the right part of the cycle, it is individually beneficial to be TFT rather than TFT-n, since TFT-n never gets cooperation on any of the last (n-1) turns.
On your other point, it’s worth noting that organisms are adaptation-executors, not fitness-maximizers; it seems easier to evolve generally altruistic values (combined with a memory of past defectors to avoid getting exploited by them or by similar agents again) than to evolve a full calculator for when defection would be truly without cost.
This “clique” solution has some problems. First, a single mutant can’t form a clique. OK, but maybe the mutant is interacting with nearby individuals, some of whom also share the mutation? That works if the nearby partners are relatives, but the difficulty there is that kin selection would already be favouring co-operation with neighbours, so how does TFT get an advantage? You can juggle with the pay-offs and the “shadow of the future” probability to try and get this to work (i.e. find a set of parameters where co-operation with neighbours via kin selection is not favoured, whereas TFT is), but it all looks a bit shaky.
Andreas Griger below suggests that the TFT mutants preferentially interact with each other rather than the TFT-n (or DefectBots) around them. This is another solution, though it adds to the overhead/complexity of a successful invader. However, it does lead to a nice testable prediction: species which practice reciprocation with non-relatives will also practice partner selection.
The point about adaptation executors not being fitness maximizers was also brought up by Unnamed below though see my response. The general issue is that citing the link is not an all-purpose excuse for maladaptation (what Richard Dawkins once referred to as the “evolution has bungled again” explanation). In particular you might want to see a paper by Fehr and Henrich Is Strong Reciprocity a maladaptation? which looks at the maladaptation hypothesis in detail and shows that it just doesn’t fit the evidence. Definitely worth a read if you have time.