If you can trade cash conditionally on behavior, it’s trivial to fix the prisoners’ dilemma. Each of you offers to pay the other a fee to cooperate, then you cooperate and you ‘both pay’ which balances out. PD is only hard when you can’t do that.
Unless I’m missing something, the promise of cash transfers alone doesn’t fix the prisoners’ dilemma. If Alice expects Bob to cooperate and pay her $100 iff both cooperate, Alice’s best response is to cooperate and then pay Bob nothing. The standard logic of best responses makes everything unravel back to defection.
To fix incentives with conditional transfers, players need to commit to them. If they can do that though, why not just commit to cooperation directly? On decision-theoretic grounds alone, I don’t see why one would be easier than another. External commitment devices like escrow (through a trusted third party or cryptography) do rely on cash.
We agree on what the final payoffs in the PD should be, whether or not transfers make it easier. The point of this post is what payoffs agents should commit to in general two-person games with transfers, however they accomplish that commitment.
I think the point is that in PD symmetry+precommitment ⇒ cooperation, and asymmetry + precommitment = symmetry (this is the “trivial fix”), so asymmetry + precommitment ⇒ cooperation.
Kinda. Benja pointed out the asymmetry + precommitment = symmetry part; I pointed out the symmetry + precommitment part. It just seems that precommitment + free trade makes all sorts of problems rather easy. Not all, of course—just who do you precommit to equalizing with, say, and of course how do you calibrate your relative utilities.
If you can trade cash conditionally on behavior, it’s trivial to fix the prisoners’ dilemma. Each of you offers to pay the other a fee to cooperate, then you cooperate and you ‘both pay’ which balances out. PD is only hard when you can’t do that.
Unless I’m missing something, the promise of cash transfers alone doesn’t fix the prisoners’ dilemma. If Alice expects Bob to cooperate and pay her $100 iff both cooperate, Alice’s best response is to cooperate and then pay Bob nothing. The standard logic of best responses makes everything unravel back to defection.
To fix incentives with conditional transfers, players need to commit to them. If they can do that though, why not just commit to cooperation directly? On decision-theoretic grounds alone, I don’t see why one would be easier than another. External commitment devices like escrow (through a trusted third party or cryptography) do rely on cash.
We agree on what the final payoffs in the PD should be, whether or not transfers make it easier. The point of this post is what payoffs agents should commit to in general two-person games with transfers, however they accomplish that commitment.
...so? What you say is true but seems entirely irrelevant to the question what the superrational outcome in an asymmetric game should be.
I think the point is that in PD symmetry+precommitment ⇒ cooperation, and asymmetry + precommitment = symmetry (this is the “trivial fix”), so asymmetry + precommitment ⇒ cooperation.
Kinda. Benja pointed out the asymmetry + precommitment = symmetry part; I pointed out the symmetry + precommitment part. It just seems that precommitment + free trade makes all sorts of problems rather easy. Not all, of course—just who do you precommit to equalizing with, say, and of course how do you calibrate your relative utilities.