Here's my response to the rest of your post. I think you're right that with two identical deterministic computations, there is no need to apply game theory. I think in that case you should consider yourself to be both of them. It would not work to think there's 50% chance you're one and 50% chance you're the other.
In my analysis I did not make the assumption that all of the copies are deterministic and have no access to independent random numbers, so game theoretic considerations do apply. In the first scenario where your copies are trying to win prizes for you, game theory lead to the same conclusion. In the Amnesiac Prisoner's Dillemma, the assumption is that the players are different people who have suffered temporary amnesia, not copies of one original person, so they can't be identical deterministic computations. On Wed, Jul 17, 2002 at 06:49:04PM -0700, Hal Finney wrote: > The point is that in one of those two states, his decision does in > fact have a causal effect on the outcome. It is the direct effect of > his decision that lets the experimenter fill the boxes. So from his > subjective perspective, where he doesn't know if this is the first or > second run, he can at least figure that there is a 50% chance that his > decision has a causal effect on the outcome. It seems to me that this > might be enough to justify choosing one box even from a causal analysis. Again, I think you need to think of yourself as both runs, so there is probability 1 that your decision has a causal effect on the amount of money in box 2. Otherwise, how do you compute the expected payoff of chosing only one box?
