Playing prisoner’s dilemma against a copy of yourself is mostly the same problem as Newcomb’s. Instead of Omega’s prediction being perfectly correlated with your choice, you have an identical agent whose choice will be perfectly correlated with yours—or, possibly, randomly distributed in the same manner. If you can also assume that both copies know this with certainty, then you can do the exact same analysis as for Newcomb’s problem.
Whether you have a prediction made by an Omega or a decision made by a copy really does not matter, as long as they both are automatically going to be the same as your own choice, by assumption in the problem statement.
The copy problem is well specified, though. Unlike the “predictor”. I clarified more in private. The worst part about Newcomb’s is that all the ex religious folks seem to substitute something they formerly knew as ‘god’ for predictor. The agent can also be further specified; e.g. as a finite Turing machine made of cogs and levers and tape with holes in it. The agent can’t simulate itself directly, of course, but it knows some properties of itself without simulation. E.g. it knows that in the alternative that it chooses to cooperate, it’s initial state was in set A—the states that result in cooperation, in the alternative that it chooses to defect, it’s initial state was in set B—the states that result in defection, and that no state is in both sets.
Playing prisoner’s dilemma against a copy of yourself is mostly the same problem as Newcomb’s. Instead of Omega’s prediction being perfectly correlated with your choice, you have an identical agent whose choice will be perfectly correlated with yours—or, possibly, randomly distributed in the same manner. If you can also assume that both copies know this with certainty, then you can do the exact same analysis as for Newcomb’s problem.
Whether you have a prediction made by an Omega or a decision made by a copy really does not matter, as long as they both are automatically going to be the same as your own choice, by assumption in the problem statement.
The copy problem is well specified, though. Unlike the “predictor”. I clarified more in private. The worst part about Newcomb’s is that all the ex religious folks seem to substitute something they formerly knew as ‘god’ for predictor. The agent can also be further specified; e.g. as a finite Turing machine made of cogs and levers and tape with holes in it. The agent can’t simulate itself directly, of course, but it knows some properties of itself without simulation. E.g. it knows that in the alternative that it chooses to cooperate, it’s initial state was in set A—the states that result in cooperation, in the alternative that it chooses to defect, it’s initial state was in set B—the states that result in defection, and that no state is in both sets.