Newcomb’s Dilemma
Newcomb’s Dilemma is an exercise in Game Theory that involves two boxes, one that contains $1,000 and a mystery box that contains either $1 million or nothing. You are given a choice whether to pick between both boxes or just the mystery box, but you are facing an adversarial host who is incredibly accurate (say 95% accuracy) at predicting what you will choose. If the host predicts that you will choose both boxes, he places nothing in the mystery box whereas if he predicts that you will choose just the mystery box he will place $1 million in it. Note that at the time you actually make your choice, the host has already determined what is in the mystery box. What is the correct course of action in this game?
The interesting part of this is that everyone sees an obvious answer, but the obvious answer is different for different people. There are two schools of thought: First we will the expected payoff of this game. In this case, the expected payout of choosing one box would be: .95 x $1,000,000 + .05 = $950,000 Meanwhile, the expected payout of choosing two boxes would be: .95 x $1,000 + .05 x $1,000,000 = $51,000. This line of reasoning suggests that it is rational to choose only one box, because the expected payout is higher.
But this seems counter intuitive when we examine what we learned in class, the theory of dominant strategies. At the time of actually choosing the box, the contents of both boxes are fixed. This means that choosing both boxes is a dominant strategy because you will get the contents of both boxes which will always be greater than or equal to the contents of just one! But again, this seems to contradict the previous payoff matrix.
This dilemma was first introduced by William Newcomb and Robert Nozick and analyzed in this article by Franz Kiekeben: http://www.kiekeben.com/newcomb.html