Since prisoners’ dilemmas are always finite in practice, and always have been (we are mortal, and the Sun will blow up at some point), this raises the question of why we actually co-operate in practice. Why is TFT, or something very like it, still around?
In general, Nash equlibria in non-zero-sum games don’t mean much if the other player isn’t a rational game theoretician. If you can for whatever reasons expect the other player to cooperate the first round, defecting is obviously a mistake.
Also, since you’re discussing semi-evolutionary adaption of strategies (like TFT-2D replacing TFT-1D), keep in mind that TFT-nD with sufficiently high n will lose against pure TFT with sufficiently high population. If you’re interested in how selective IPD works, you might want to skim over this post.
I’ve read the link, and my response is similar to the one to orthonormal further up the thread. I’m struggling to understand how TFT can invade a population of TFT-nD, because it will not satisfy what the link calls the “survival rule”:
Survival Rule: For A in this scenario not to go extinct regardless of initial population, it must score at least equally high against X as X does against itself, and if it doesn’t score higher, it must score at least equally high against itself as X does against itself while not losing direct encounters.
In the particular case, A is TFT and X is TFT-nD. But TFT has strictly lower fitness against TFT-nD than TFT-nD has against itself, so it won’t pass the survival rule. A rare mutant practising TFT in a population of TFT-nD will go extinct.
I can’t see any way round this except some sort of Group selection argument, whereby the TFT mutants cluster and interact mostly with each other until they meet the Threshold rule, at which point they can go on to dominate the whole population:
Threshold rule: If A fulfills the conditions for dominance but not the conditions for survival (i.e. it scores less against X than X does against itself), it will need a certain threshold to avoid extinction and achieve dominance.
Such a Group selection approach could work, but it seems frankly dubious. While it could happen once or twice (e.g. enough to get TFT going in the first place), it looks like a real stretch to claim it hapens repeatedly, so ensuring a rock-scissors-paper cycle is preserved between TFT and various flavours of TFT-nD.
Am I just missing something really obvious here? Hardly anyone else on the thread seems to recognise this as a problem.
You are correct in saying that TFT cannot strictly evolve (starting with 0 population) from TFT-nD in that case. However, for increasing n and number of rounds the extinction threshold becomes sufficiently small. Maybe more importantly, unlike in the type of tournaments discussed in the link, real people can identify other people outside the game. There’s nothing to stop a player from playing different strategies depending on which group of people the other player belongs to. If we assume a prehistoric tribe where people defect a lot, just two players cooperating with each other for a little longer than the others have found a winning strategy already. In addition to that, it also becomes attractive for other players to join their little clique.
Basically, this leads us to a form of meta-TFT—”If you defect first in interpersonal interaction, you are not in our little group of cooperators anymore.” So in a tribe of people who know each other and need to interact with certain other people within that tribe, cooperation is the winning strategy for everyone. Inter-tribe competition amplifies this.
The larger the tribe and the easier it is to leave the tribe, the smaller the benefits of cooperation become. But even in modern society most people are part of such tribe-like groups where they are forced or have sufficient motivation to interact with certain other people—family, kindergarten, school, workplace, clubs, whatever. People learn to achieve their goals within these groups from a very young age by forming cliques, so TFT-like strategies are naturally adopted.
Thanks for acknowledging that there is an issue here, and something worth explaining. Upvoted.
Your suggested explanation for how TFT invades TFT-nD requires something more than just TFT here. As well as a cluster entry (at least two initially, not just one mutant), it also requires an ability to select preferred partners (i.e. the two co-operators preferentially select each other), and a reputational system (to help decide which partners to select).
This raises a question which could be tested: do all species that engage in reciprocal altruism have those additional features i.e. preferred partners and reputation? Do vampire bats? (It seems quite an overhead for a bat, doesn’t it?) Can TFT plausibly invade with fewer features?
Another concern would be how TFT enters a population of DefectBots in the first place… It would require a major (and implausible) mutation to introduce all these features at once. Even TFT by itself (without the extra features) is significantly more complicated than a DefectBot, which raises an origin question : what series of mutations can put TFT together starting from a DefectBot, and how are the intermediates favoured? Does machinery for kin selection need to evolve first and then get re-purposed? (This leads to another prediction, that reciprocating species also have to practice kin selection, or at least have ancestors which did).
I disagree with you that defecting is the default action for animals in state/herd/pack/tribe-like communities. Unless you want to discuss how these kind of communities could form in the first place, it seems to me that the question how TFT can prohibit TFT-nD from invading is much more relevant than how TFT can invade TFT-nD. And that is ultimately the point—as I’ve explained above, for a tribe-forming species TFT (or meta-TFT) is an evolutionary stable strategy.
I disagree with you that defecting is the default action for animals in state/herd/pack/tribe-like communities. Unless you want to discuss how these kind of communities could form in the first place,
Are you claiming here that all herd or pack species are practising TFT, or that it is the default for herd/pack species? That seems empirically dubious: my understanding was that herd or pack species are mainly held together either by kin selection (the pack consists of close relatives) or by simple mutualism (e.g. being in the herd protects against predation, and it would be suicide to leave) rather than by something as sophisticated as TFT. It’s a while since I looked at the literature, but species practising reciprocal altruism with non-relatives seem to be fairly rare. But if you can cite studies, that would be helpful.
If you can for whatever reasons expect the other player to cooperate the first round, defecting is obviously a mistake.
No it isn’t. All else being equal knowing that the other player will cooperate on the first round (independently of what you do on the first round) is a reason to defect. It is the expectations of conditional cooperations on later rounds that make cooperation seem wise.
Of course this is a matter of conditional cooperation, this is fixed-length IPD after all. I don’t see your point?
Your claim, quoted in the grandparent, is false. You should have instead claimed something that is true. This would seem to be the implied point when correcting errors.
If you don’t have anything useful to post, maybe better not post anything?
It is the expectations of conditional cooperations on later rounds that make cooperation seem wise.
No, it is the possibility of conditional cooperations on later rounds that make cooperation seem wise. You don’t “expect” anything the first round. Your claim is false; you should have instead claimed something that is true.
All else being equal knowing that the other player will cooperate on the first round (independently of what you do on the first round) is a reason to defect.
If you have no knowledge about your opponent except for his first move, then him cooperating is no reason for you to defect. If anything, you might defect regardless of your opponent’s first move, but defecting because of cooperation is irrational and insane. Your claim is false, etc pp.
Excuse me for calling into question your ability to comprehend IPD, but since you were the one to submit DefectBot to the tournament that seems justified to me at this point.
If you can for whatever reasons expect the other player to cooperate the first round, defecting is obviously a mistake.
...while clearly an error, was at least a comparatively minor one. I, and probably most readers, assumed that you knew the basics but were just slightly lax in your wording. I expected you to simply revise it to, for example, something along the lines of:
If you can for whatever reasons expect the other player to act similarly to TFT-nD with sufficiently small n, defecting is obviously a mistake.
You instead chose to defend the original, overly generalized and unqualified position using a series of non-sequitur status challenges. That wasn’t a good decision.
Excuse me for calling into question your ability to comprehend IPD, but since you were the one to submit DefectBot to the tournament that seems justified to me at this point.
As I said, I originally had the impression that you comprehended the basics but were being careless. I now agree that at least one of us is fundamentally confused.
If you have no knowledge about your opponent except for his first move, then him cooperating is no reason for you to defect. If anything, you might defect regardless of your opponent’s first move, but defecting because of cooperation is irrational and insane.
No. Knowledge that the other will cooperate on the first round regardless of what you do does, in fact, eliminate one of the strongest reasons for cooperating. In particular, that you believe they are able to make predictions about you and act accordingly—ie. that you expect them to have the same prediction capability that you have ascribed to yourself.
I’ve read your post a few times, but it still seems like you’re saying that the possibility of your opponent being an omniscient maximiser is your main reason for cooperating. So if you knew you were to play against Omega-Clippy, who can predict all your possible actions right from the start, because of that you would play some kind of TFT? Did I get that right?
In general, Nash equlibria in non-zero-sum games don’t mean much if the other player isn’t a rational game theoretician. If you can for whatever reasons expect the other player to cooperate the first round, defecting is obviously a mistake.
Also, since you’re discussing semi-evolutionary adaption of strategies (like TFT-2D replacing TFT-1D), keep in mind that TFT-nD with sufficiently high n will lose against pure TFT with sufficiently high population. If you’re interested in how selective IPD works, you might want to skim over this post.
I’ve read the link, and my response is similar to the one to orthonormal further up the thread. I’m struggling to understand how TFT can invade a population of TFT-nD, because it will not satisfy what the link calls the “survival rule”:
In the particular case, A is TFT and X is TFT-nD. But TFT has strictly lower fitness against TFT-nD than TFT-nD has against itself, so it won’t pass the survival rule. A rare mutant practising TFT in a population of TFT-nD will go extinct.
I can’t see any way round this except some sort of Group selection argument, whereby the TFT mutants cluster and interact mostly with each other until they meet the Threshold rule, at which point they can go on to dominate the whole population:
Such a Group selection approach could work, but it seems frankly dubious. While it could happen once or twice (e.g. enough to get TFT going in the first place), it looks like a real stretch to claim it hapens repeatedly, so ensuring a rock-scissors-paper cycle is preserved between TFT and various flavours of TFT-nD.
Am I just missing something really obvious here? Hardly anyone else on the thread seems to recognise this as a problem.
You are correct in saying that TFT cannot strictly evolve (starting with 0 population) from TFT-nD in that case. However, for increasing n and number of rounds the extinction threshold becomes sufficiently small. Maybe more importantly, unlike in the type of tournaments discussed in the link, real people can identify other people outside the game. There’s nothing to stop a player from playing different strategies depending on which group of people the other player belongs to. If we assume a prehistoric tribe where people defect a lot, just two players cooperating with each other for a little longer than the others have found a winning strategy already. In addition to that, it also becomes attractive for other players to join their little clique.
Basically, this leads us to a form of meta-TFT—”If you defect first in interpersonal interaction, you are not in our little group of cooperators anymore.” So in a tribe of people who know each other and need to interact with certain other people within that tribe, cooperation is the winning strategy for everyone. Inter-tribe competition amplifies this.
The larger the tribe and the easier it is to leave the tribe, the smaller the benefits of cooperation become. But even in modern society most people are part of such tribe-like groups where they are forced or have sufficient motivation to interact with certain other people—family, kindergarten, school, workplace, clubs, whatever. People learn to achieve their goals within these groups from a very young age by forming cliques, so TFT-like strategies are naturally adopted.
Thanks for acknowledging that there is an issue here, and something worth explaining. Upvoted.
Your suggested explanation for how TFT invades TFT-nD requires something more than just TFT here. As well as a cluster entry (at least two initially, not just one mutant), it also requires an ability to select preferred partners (i.e. the two co-operators preferentially select each other), and a reputational system (to help decide which partners to select).
This raises a question which could be tested: do all species that engage in reciprocal altruism have those additional features i.e. preferred partners and reputation? Do vampire bats? (It seems quite an overhead for a bat, doesn’t it?) Can TFT plausibly invade with fewer features?
Another concern would be how TFT enters a population of DefectBots in the first place… It would require a major (and implausible) mutation to introduce all these features at once. Even TFT by itself (without the extra features) is significantly more complicated than a DefectBot, which raises an origin question : what series of mutations can put TFT together starting from a DefectBot, and how are the intermediates favoured? Does machinery for kin selection need to evolve first and then get re-purposed? (This leads to another prediction, that reciprocating species also have to practice kin selection, or at least have ancestors which did).
I disagree with you that defecting is the default action for animals in state/herd/pack/tribe-like communities. Unless you want to discuss how these kind of communities could form in the first place, it seems to me that the question how TFT can prohibit TFT-nD from invading is much more relevant than how TFT can invade TFT-nD. And that is ultimately the point—as I’ve explained above, for a tribe-forming species TFT (or meta-TFT) is an evolutionary stable strategy.
Are you claiming here that all herd or pack species are practising TFT, or that it is the default for herd/pack species? That seems empirically dubious: my understanding was that herd or pack species are mainly held together either by kin selection (the pack consists of close relatives) or by simple mutualism (e.g. being in the herd protects against predation, and it would be suicide to leave) rather than by something as sophisticated as TFT. It’s a while since I looked at the literature, but species practising reciprocal altruism with non-relatives seem to be fairly rare. But if you can cite studies, that would be helpful.
No it isn’t. All else being equal knowing that the other player will cooperate on the first round (independently of what you do on the first round) is a reason to defect. It is the expectations of conditional cooperations on later rounds that make cooperation seem wise.
Of course this is a matter of conditional cooperation, this is fixed-length IPD after all. I don’t see your point?
Your claim, quoted in the grandparent, is false. You should have instead claimed something that is true. This would seem to be the implied point when correcting errors.
If you don’t have anything useful to post, maybe better not post anything?
No, it is the possibility of conditional cooperations on later rounds that make cooperation seem wise. You don’t “expect” anything the first round. Your claim is false; you should have instead claimed something that is true.
If you have no knowledge about your opponent except for his first move, then him cooperating is no reason for you to defect. If anything, you might defect regardless of your opponent’s first move, but defecting because of cooperation is irrational and insane. Your claim is false, etc pp.
Excuse me for calling into question your ability to comprehend IPD, but since you were the one to submit DefectBot to the tournament that seems justified to me at this point.
Your original claim:
...while clearly an error, was at least a comparatively minor one. I, and probably most readers, assumed that you knew the basics but were just slightly lax in your wording. I expected you to simply revise it to, for example, something along the lines of:
You instead chose to defend the original, overly generalized and unqualified position using a series of non-sequitur status challenges. That wasn’t a good decision.
As I said, I originally had the impression that you comprehended the basics but were being careless. I now agree that at least one of us is fundamentally confused.
No. Knowledge that the other will cooperate on the first round regardless of what you do does, in fact, eliminate one of the strongest reasons for cooperating. In particular, that you believe they are able to make predictions about you and act accordingly—ie. that you expect them to have the same prediction capability that you have ascribed to yourself.
I’ve read your post a few times, but it still seems like you’re saying that the possibility of your opponent being an omniscient maximiser is your main reason for cooperating. So if you knew you were to play against Omega-Clippy, who can predict all your possible actions right from the start, because of that you would play some kind of TFT? Did I get that right?