jimmy

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What counts as 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.