Suppose b “knows” that Omega runs this experiment for all programs b. Then the optimal behaviour for a competent b (by a ridiculously small margin) is to 1-box.
Suppose b suspects that box-choosing programs are slightly less likely to be run if they 1-box on equal inputs. Then the optimal behaviour for b is to 2-box, because the average extra payoff for 1-boxing on equal inputs is utterly insignificant while the average penalty for not being chosen to run is very much greater. Anything that affects probability of being run as box-chooser with probability greater than 1000/|P| (which is on the order of 1/10^10^10^10^100) matters far more than what the program actually does.
In the original Newcombe problem, you know that you are going to get money based on your decision. In this problem, a running program does not know this. It doesn’t know whether it’s a or b or both, and every method for selecting a box-chooser is a different problem with different optimal strategies.
I’ll try to make it clearer:
Suppose b “knows” that Omega runs this experiment for all programs b. Then the optimal behaviour for a competent b (by a ridiculously small margin) is to 1-box.
Suppose b suspects that box-choosing programs are slightly less likely to be run if they 1-box on equal inputs. Then the optimal behaviour for b is to 2-box, because the average extra payoff for 1-boxing on equal inputs is utterly insignificant while the average penalty for not being chosen to run is very much greater. Anything that affects probability of being run as box-chooser with probability greater than 1000/|P| (which is on the order of 1/10^10^10^10^100) matters far more than what the program actually does.
In the original Newcombe problem, you know that you are going to get money based on your decision. In this problem, a running program does not know this. It doesn’t know whether it’s a or b or both, and every method for selecting a box-chooser is a different problem with different optimal strategies.