I just came up with another argument why 2 is nicer than 1: the predictor can use 2 multiple times and get knowledge that’s similar to 1, but without the infinite precision that makes 1 problematic.
As for 3, it can also be translated into single player game theory by doing another kind of modification on the game tree, and gives the same answers as 2 in NP and CM. But 2 is more in line with the rest of game theory where players can have private randomness, and it’s what you get when you replace predictors with amnesia or Nash equilibrium prediction.
I just came up with another argument why 2 is nicer than 1: the predictor can use 2 multiple times and get knowledge that’s similar to 1, but without the infinite precision that makes 1 problematic.
As for 3, it can also be translated into single player game theory by doing another kind of modification on the game tree, and gives the same answers as 2 in NP and CM. But 2 is more in line with the rest of game theory where players can have private randomness, and it’s what you get when you replace predictors with amnesia or Nash equilibrium prediction.