As others have mentioned, there’s an interpersonal utility comparison problem. In general, it is hard to determine how to weight utility between people. If I want to trade with you but you’re not home, I can leave some amount of potatoes for you and take some amount of your milk. At what ratio of potatoes to milk am I “cooperating” with you, and at what level am I a thieving defector? If there’s a market down the street that allows us to trade things for money then it’s easy to do these comparisons and do Coasian payments as necessary to coordinate on maximizing the size of the pie. If we’re on a deserted island together it’s harder. Trying to drive a hard bargain and ask for more milk for my potatoes is a qualitatively different thing when there’s no agreed upon metric you can use to say that I’m trying to “take more than I give”.
Here is an interesting and hilarious experiment about how people play an iterated asymmetric prisoner’s dilemma. The reason it wasn’t more pure cooperation is that due to the asymmetry there was a disagreement between the players about what was “fair”. AA thought JW should let him hit “D” some fraction of the time to equalize the payouts, and JW thought that “C/C” was the right answer to coordinate towards. If you read their comments, it’s clear that AA thinks he’s cooperating in the larger game, and that his “D” aren’t anti-social at all. He’s just trying to get a “fair” price for his potatoes, and he’s mistaken about what that is. JW, on the other hand, is explicitly trying use his Ds to coax A into cooperation. This conflict is better understood as a disagreement over where on the Pareto frontier (“at which price”) to trade than it is about whether it’s better to cooperate with each other or defect.
In real life problems, it’s usually not so obvious what options are properly thought of as “C” or “D”, and when trying to play “tit for tat with forgiveness” we have to be able to figure out what actually counts as a tit to tat. To do so, we need to look at the extent to which the person is trying to cooperate vs trying to get away with shirking their duty to cooperate. In this case, AA was trying to cooperate, and so if JW could have talked to him and explained why C/C was the right cooperative solution, he might have been able to save the lossy Ds. If AA had just said “I think I can get away with stealing more value by hitting D while he cooperates”, no amount of explaining what the right concept of cooperation looks like will fix that, so defecting as punishment is needed.
In general, the way to determine whether someone is “trying to cooperate” vs “trying to defect” is to look at how they see the payoff matrix, and figure out whether they’re putting in effort to stay on the Pareto frontier or to go below it. If their choice shows that they are being diligent to give you as much as possible without giving up more themselves, then they may be trying to drive a hard bargain, but at least you can tell that they’re trying to bargain. If their chosen move is conspicuously below (their perception of) the Pareto frontier, then you can know that they’re either not-even-trying, or they’re trying to make it clear that they’re willing to harm themselves in order to harm you too.
In games like real life versions of “stag hunt”, you don’t want to punish people for not going stag hunting when it’s obvious that no one else is going either and they’re the one expending effort to rally people to coordinate in the first place. But when someone would have been capable of nearly assuring cooperation if they did their part and took an acceptable risk when it looked like it was going to work, then it makes sense to describe them as “defecting” when they’re the one that doesn’t show up to hunt the stag because they’re off chasing rabbits.
”Deliberately sub-Pareto move” I think is a pretty good description of the kind of “defection” that means you’re being tatted, and “negligently sub-Pareto” is a good description of the kind of tit to tat.
As others have mentioned, there’s an interpersonal utility comparison problem. In general, it is hard to determine how to weight utility between people.
I actually don’t think this is a problem for the use case I have in mind. I’m not trying to solve the comparison problem. This work formalizes: “given a utility weighting, what is defection?”. I don’t make any claim as to what is “fair” / where that weighting should come from. I suppose in the EGTA example, you’d want to make sure eg reward functions are identical.
“Deliberately sub-Pareto move” I think is a pretty good description of the kind of “defection” that means you’re being tatted, and “negligently sub-Pareto” is a good description of the kind of tit to tat.
Defection doesn’t always have to do with the Pareto frontier—look at PD, for example. (C,C), (C,D), (D,C) are usually all Pareto optimal.
I actually don’t think this is a problem for the use case I have in mind. I’m not trying to solve the comparison problem. This work formalizes: “given a utility weighting, what is defection?”. I don’t make any claim as to what is “fair” / where that weighting should come from. I suppose in the EGTA example, you’d want to make sure eg reward functions are identical.
This strikes me as a particularly large limitation. If you don’t have any way of creating meaningful weightings of utility between agents then you can’t get anything meaningful out. If you’re allowed to play with that free parameter then you can simply say “I’m not a utility monster, this genuinely impacts me more than you [because I said so!]” and your actual outcomes aren’t constrained at all.
Defection doesn’t always have to do with the Pareto frontier—look at PD, for example. (C,C), (C,D), (D,C) are usually all Pareto optimal.
That’s why I talk about “in the larger game” and use scare quotes on “defection”. I think the word has to many different connotations and needs to be unpacked a bit.
The dictionary definition, for example, is:
A lack: a failure; especially, failure in the performance of duty or obligation.
n.The act of abandoning a person or a cause to which one is bound by allegiance or duty, or to which one has attached himself; a falling away; apostasy; backsliding.
n.Act of abandoning a person or cause to which one is bound by allegiance or duty, or to which one has attached himself; desertion; failure in duty; a falling away; apostasy; backsliding.
This all fits what I was talking about, and the fact that the options in prisoners dilemma are traditionally labeled “Cooperate” and “Defect” doesn’t mean they fit the definition. It smuggles in these connotations when they do not necessarily apply.
The idea of using tit for tat to encourage cooperation requires determining what ones “duty” is and what “failing” this duty is, and “doesn’t maximize total utility” does not actually work as a definition for this purpose because you still have to figure out how to do that scaling.
Using the Pareto frontier allows you to distinguish between cooperative and non-cooperative behavior without having to make assumptions/claims about whose preferences are more “valid”. This is really important for any real world application, because you don’t actually get those scalings on a silver platter, and therefore need a way to distinguish between “cooperative” and “selfishly destructive” behavior as separate from “trying to claim a higher weight to one’s own utility”.
This strikes me as a particularly large limitation. If you don’t have any way of creating meaningful weightings of utility between agents then you can’t get anything meaningful out. If you’re allowed to play with that free parameter then you can simply say “I’m not a utility monster, this genuinely impacts me more than you [because I said so!]” and your actual outcomes aren’t constrained at all.
This just isn’t what I want to use the definition for. It’s meant to be descriptive, not prescriptive.
Similarly, while other definitions of “defection” also exist, I’m interested in the sense I outlined in the post. In particular, I’m not interested in any proposed definition that labels defection in PD as not-defection.
As others have mentioned, there’s an interpersonal utility comparison problem. In general, it is hard to determine how to weight utility between people. If I want to trade with you but you’re not home, I can leave some amount of potatoes for you and take some amount of your milk. At what ratio of potatoes to milk am I “cooperating” with you, and at what level am I a thieving defector? If there’s a market down the street that allows us to trade things for money then it’s easy to do these comparisons and do Coasian payments as necessary to coordinate on maximizing the size of the pie. If we’re on a deserted island together it’s harder. Trying to drive a hard bargain and ask for more milk for my potatoes is a qualitatively different thing when there’s no agreed upon metric you can use to say that I’m trying to “take more than I give”.
Here is an interesting and hilarious experiment about how people play an iterated asymmetric prisoner’s dilemma. The reason it wasn’t more pure cooperation is that due to the asymmetry there was a disagreement between the players about what was “fair”. AA thought JW should let him hit “D” some fraction of the time to equalize the payouts, and JW thought that “C/C” was the right answer to coordinate towards. If you read their comments, it’s clear that AA thinks he’s cooperating in the larger game, and that his “D” aren’t anti-social at all. He’s just trying to get a “fair” price for his potatoes, and he’s mistaken about what that is. JW, on the other hand, is explicitly trying use his Ds to coax A into cooperation. This conflict is better understood as a disagreement over where on the Pareto frontier (“at which price”) to trade than it is about whether it’s better to cooperate with each other or defect.
In real life problems, it’s usually not so obvious what options are properly thought of as “C” or “D”, and when trying to play “tit for tat with forgiveness” we have to be able to figure out what actually counts as a tit to tat. To do so, we need to look at the extent to which the person is trying to cooperate vs trying to get away with shirking their duty to cooperate. In this case, AA was trying to cooperate, and so if JW could have talked to him and explained why C/C was the right cooperative solution, he might have been able to save the lossy Ds. If AA had just said “I think I can get away with stealing more value by hitting D while he cooperates”, no amount of explaining what the right concept of cooperation looks like will fix that, so defecting as punishment is needed.
In general, the way to determine whether someone is “trying to cooperate” vs “trying to defect” is to look at how they see the payoff matrix, and figure out whether they’re putting in effort to stay on the Pareto frontier or to go below it. If their choice shows that they are being diligent to give you as much as possible without giving up more themselves, then they may be trying to drive a hard bargain, but at least you can tell that they’re trying to bargain. If their chosen move is conspicuously below (their perception of) the Pareto frontier, then you can know that they’re either not-even-trying, or they’re trying to make it clear that they’re willing to harm themselves in order to harm you too.
In games like real life versions of “stag hunt”, you don’t want to punish people for not going stag hunting when it’s obvious that no one else is going either and they’re the one expending effort to rally people to coordinate in the first place. But when someone would have been capable of nearly assuring cooperation if they did their part and took an acceptable risk when it looked like it was going to work, then it makes sense to describe them as “defecting” when they’re the one that doesn’t show up to hunt the stag because they’re off chasing rabbits.
”Deliberately sub-Pareto move” I think is a pretty good description of the kind of “defection” that means you’re being tatted, and “negligently sub-Pareto” is a good description of the kind of tit to tat.
I actually don’t think this is a problem for the use case I have in mind. I’m not trying to solve the comparison problem. This work formalizes: “given a utility weighting, what is defection?”. I don’t make any claim as to what is “fair” / where that weighting should come from. I suppose in the EGTA example, you’d want to make sure eg reward functions are identical.
Defection doesn’t always have to do with the Pareto frontier—look at PD, for example. (C,C), (C,D), (D,C) are usually all Pareto optimal.
This strikes me as a particularly large limitation. If you don’t have any way of creating meaningful weightings of utility between agents then you can’t get anything meaningful out. If you’re allowed to play with that free parameter then you can simply say “I’m not a utility monster, this genuinely impacts me more than you [because I said so!]” and your actual outcomes aren’t constrained at all.
That’s why I talk about “in the larger game” and use scare quotes on “defection”. I think the word has to many different connotations and needs to be unpacked a bit.
The dictionary definition, for example, is:
This all fits what I was talking about, and the fact that the options in prisoners dilemma are traditionally labeled “Cooperate” and “Defect” doesn’t mean they fit the definition. It smuggles in these connotations when they do not necessarily apply.
The idea of using tit for tat to encourage cooperation requires determining what ones “duty” is and what “failing” this duty is, and “doesn’t maximize total utility” does not actually work as a definition for this purpose because you still have to figure out how to do that scaling.
Using the Pareto frontier allows you to distinguish between cooperative and non-cooperative behavior without having to make assumptions/claims about whose preferences are more “valid”. This is really important for any real world application, because you don’t actually get those scalings on a silver platter, and therefore need a way to distinguish between “cooperative” and “selfishly destructive” behavior as separate from “trying to claim a higher weight to one’s own utility”.
This just isn’t what I want to use the definition for. It’s meant to be descriptive, not prescriptive.
Similarly, while other definitions of “defection” also exist, I’m interested in the sense I outlined in the post. In particular, I’m not interested in any proposed definition that labels defection in PD as not-defection.