It’s tempting to take a step back and consider the coordination game from the point of view of the agent before-observation, as it gives a nice equivalence between the copies, control over the consequences for both copies from a common source. This comes with a simple algorithm, an actual explanation. But as I suspect you intended to communicate in this comment, this is not very interesting, because it’s not a general case: in two-player games the other player is not your copy, and wasn’t one any time previous. But if we try to consider the actions of agent after-observation, of the two copies diverged, there seems to be no nice solution anymore.
It’s clear how the agent before-observations controls the copies after, and so how its decisions about the strategy of reacting to future observations control both copies, coordinate them. It’s far from clear how a copy that received one observation can control a copy that received the other observation. Parts control the whole, but not conversely. Yet the coordination problem could be posed about two agents that have nothing in common, and we’d expect there to be a solution to that as well. Thus I expect the coordination problem with two copies to have a local solution, apart from the solution of deciding in advance, as you describe in the post.
My comment to which you linked is clearly flawed in at least one respect: it assumes that to control a structure B with agent A, B has to be defined in terms of A. This is still an explicit control mindset, what I call acausal control, but it’s wrong, not as general as ambient control, where you are allowed to discover new dependencies, or UDT, where the discovery of new dependencies is implicit in mathematical intuition.
It’ll take much better understanding of theories of consequences, the process of their exploration, preference defined over them, to give specific examples, and I don’t expect these examples to be transparent (but maybe there is a simple proof that the decisions will be correct, that doesn’t point out the specific details of the decision-making process).
It’s tempting to take a step back and consider the coordination game from the point of view of the agent before-observation, as it gives a nice equivalence between the copies, control over the consequences for both copies from a common source. This comes with a simple algorithm, an actual explanation. But as I suspect you intended to communicate in this comment, this is not very interesting, because it’s not a general case: in two-player games the other player is not your copy, and wasn’t one any time previous. But if we try to consider the actions of agent after-observation, of the two copies diverged, there seems to be no nice solution anymore.
It’s clear how the agent before-observations controls the copies after, and so how its decisions about the strategy of reacting to future observations control both copies, coordinate them. It’s far from clear how a copy that received one observation can control a copy that received the other observation. Parts control the whole, but not conversely. Yet the coordination problem could be posed about two agents that have nothing in common, and we’d expect there to be a solution to that as well. Thus I expect the coordination problem with two copies to have a local solution, apart from the solution of deciding in advance, as you describe in the post.
My comment to which you linked is clearly flawed in at least one respect: it assumes that to control a structure B with agent A, B has to be defined in terms of A. This is still an explicit control mindset, what I call acausal control, but it’s wrong, not as general as ambient control, where you are allowed to discover new dependencies, or UDT, where the discovery of new dependencies is implicit in mathematical intuition.
It’ll take much better understanding of theories of consequences, the process of their exploration, preference defined over them, to give specific examples, and I don’t expect these examples to be transparent (but maybe there is a simple proof that the decisions will be correct, that doesn’t point out the specific details of the decision-making process).