What does Newcomb’s paradox teach us?

Newcomb’s paradox highlights an apparent conflict involving the ax-ioms of game theory. It concerns a game in which you choose to take either one or both of two closed boxes. However before you choose, a prediction algorithm deduces your choice, and fills the two boxes based on that deduc-tion. The paradox is that game theory appears to provide two conflicting recommendations for what choice you should make in this situation. Here we analyze Newcomb’s paradox using a recently introduced extension of game theory in which the players set conditional probability distributions in a Bayes net. Using this extended game theory, we show that the two game theory recommendations in Newcomb’s scenario implicitly assume different Bayes nets relating the random variables of your choice and the algorithm’s prediction. We resolve the paradox by proving that these two assumed Bayes nets are incompatible, i.e., the associated assumptions conflict. In doing this we show that the accuracy of the algorithm’s prediction, which was the focus of much previous work on Newcomb’s paradox, is irrelevant. We also show that Newcomb’s paradox is time-reversal invariant; both the paradox and its resolution are unchanged if the algorithm makes its “prediction ” after you make your choice rather than before