How does the typical construction of Newcomb’s problem handle mixed strategies?
The predictor can read your RNG, so your strategy is not really mixed. But this is a violation of game theory assumptions about the possibility of mixed strategies. If you are banned from mixed strategies, Game theory does not work so well, as I understand it.
The predictor has some utility distribution over (One box, two box) (Predict one box, Predict two box), and you can solve the Nash equilibrium, maybe to a mixed strategy equilibrium (where you pick one box the percentage) (IE. you want to one box often enough that the Predictor predicts that you will, but no more than that, based on the relative payouts)
The predictor has some policy on P(Place in box) for each P (onebox), and there the maximum utility might not be at P(onebox)
How does the typical construction of Newcomb’s problem handle mixed strategies?
The predictor can read your RNG, so your strategy is not really mixed. But this is a violation of game theory assumptions about the possibility of mixed strategies. If you are banned from mixed strategies, Game theory does not work so well, as I understand it.
The predictor has some utility distribution over (One box, two box) (Predict one box, Predict two box), and you can solve the Nash equilibrium, maybe to a mixed strategy equilibrium (where you pick one box the percentage) (IE. you want to one box often enough that the Predictor predicts that you will, but no more than that, based on the relative payouts)
The predictor has some policy on P(Place in box) for each P (onebox), and there the maximum utility might not be at P(onebox)