(Or maybe the right way to think about this is: it will have a tiny but non-zero effect, because you are one of the |P| programs, but since |P| is huge, that is ~0.)
No effect. I meant that programmer has to write from , not that is added to . Probably I should change the phrasing to make it clearer.
But the intuition that you were expressing in Question 2 (“p2 is better than p1 because it scores better”) isn’t compatible with “caring equally about all programs”. Instead, it sounds as if you positively want to score better than other programs, that is, maximize your score and minimize theirs!
No, the utility here is just the amount of money gets, whatever program it is. doesn’t get any money, it just determines what will be in the first box.
I don’t like the implied requirement “to be rational you must play at least as good as the opponent” instead of “to be rational you must play at least as good as any other agent in your place”. $9 rock gets $0 if it plays against $9 rock.
(No objection to overall no-free-lunch conclusion, though)