  In Newcomb's paradox you choose to receive either the contents of a
particular closed box, or the contents of both that closed box and another one.
Before you choose, a prediction algorithm deduces your choice, and fills the
two boxes based on that deduction. Newcomb's paradox is that game theory
appears to provide two conflicting recommendations for what choice you should
make in this scenario. We analyze Newcomb's paradox using a recent extension of
game theory in which the players set conditional probability distributions in a
Bayes net. We show that the two game theory recommendations in Newcomb's
scenario have different presumptions for what Bayes net relates your choice and
the algorithm's prediction. We resolve the paradox by proving that these two
Bayes nets are incompatible. We also show that the accuracy of the algorithm's
prediction, the focus of much previous work, is irrelevant. In addition we show
that Newcomb's scenario only provides a contradiction between game theory's
expected utility and dominance principles if one is sloppy in specifying the
underlying Bayes net. 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.
