What Does Newcomb's Paradox Teach Us?

Abstract

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.

Keywords: Newcomb's paradox, game theory, Bayes net, causality, determinism

JEL Classification: A12, C11, C70, C72