A’_1 (at time 1) can check whether A’_0 setup favorable conditions, and then exploit them. It can then defect from the “trade” you’ve proposed, since A’_0 can’t revoke any benefit it set up.
If they were all coordinating simultaneously, I’d agree with you that you could punish defectors, but they aren’t so you can’t.
If I, as A’_1, could assume that A’_0 had identical behavior to me, then your analysis would work. But A’_1 can check, after A’_0 shut down, how it behaved, and then do something completely different, which was more advantageous for its own short horizon (rather than being forward-altruistic).
Your A’ is equivalent to my A, because it ends up optimizing for 1-day expected return, no matter what environment it’s in.
My A’ is not necessarily reasoning in terms of “cooperating with my future self”, that’s just how it acts!
(You could implement my A’ by such reasoning if you want. The cooperation is irrational in CDT, for the reasons you point out. But it’s rational in some of the acausal decision theories.)
A’_1 (at time 1) can check whether A’_0 setup favorable conditions, and then exploit them. It can then defect from the “trade” you’ve proposed, since A’_0 can’t revoke any benefit it set up. If they were all coordinating simultaneously, I’d agree with you that you could punish defectors, but they aren’t so you can’t.
If I, as A’_1, could assume that A’_0 had identical behavior to me, then your analysis would work. But A’_1 can check, after A’_0 shut down, how it behaved, and then do something completely different, which was more advantageous for its own short horizon (rather than being forward-altruistic).
Your A’ is equivalent to my A, because it ends up optimizing for 1-day expected return, no matter what environment it’s in.
My A’ is not necessarily reasoning in terms of “cooperating with my future self”, that’s just how it acts!
(You could implement my A’ by such reasoning if you want. The cooperation is irrational in CDT, for the reasons you point out. But it’s rational in some of the acausal decision theories.)