This account of decision theory/game theory seems like unnecessary formalism. The single play-through token problem prisoners dilemma has 4 outcomes to consider and between those 4 outcomes, no matter what your opponent does, your outcome is better if you betray so you betray.
The difference with the mirror token problem is that you set it up so that there are explicitly only two outcomes to consider. you betray and get 100 dollars or you cooperate and get 200 dollars. Obviously you choose the one that has the higher expected value os you get 200 dollars. ... (read more)
Your solution hardcodes logical influence as causal influence; these are quite different. Suppose your twin is a light-year away from you. Are you saying that your choice now exerts a causal influence over an event which is space-like separated from you?
You sound like you're saying "you're choosing what kind of agent you want (both agents) to be"; in that case, you're looking at something more akin to Functional Decision Theory.
This account of decision theory/game theory seems like unnecessary formalism. The single play-through token problem prisoners dilemma has 4 outcomes to consider and between those 4 outcomes, no matter what your opponent does, your outcome is better if you betray so you betray.
The difference with the mirror token problem is that you set it up so that there are explicitly only two outcomes to consider. you betray and get 100 dollars or you cooperate and get 200 dollars. Obviously you choose the one that has the higher expected value os you get 200 dollars. ... (read more)