I’ve been continuing to write my decision theory notes for the decision theory course I’ve been doing this term. The course hasn’t ended up quite the way I expected. Because I wanted to go into more details on some of the fundamentals, and because I wanted to avoid heavy lifting in the mathematics, I’ve skipped anything to do with infinities. So that meant cutting countable additivity, the two-envelope problem, the St Petersburg Paradox, etc. But the flip side of that is that there’s more than originally intended on the nature of utility, and the most recent additions have been going quite slowly through the foundations of game theory.
One thing that I suspect is not news to many readers of this site, but which was very striking to me, was how much orthodox game theory resembles evidential decision theory. (Many people will be familiar with this because it is a point that Robert Stalnaker has made well. But writing the notes really drove home for me how true it is.)
It is really hard to offer a motivation for exclusively playing equilibrium strategies in one-shot zero-sum games that doesn’t look like a motivation for taking one-box in Newcomb’s problem. Since us causal decision theorists think taking one-box is irrational, this makes me very suspicious of the normative significance of equilibrium strategies in one-shot games. Of course, most real world games are not one-shot, and I can understand playing a mixed strategy in a repeated zero-sum game. But it is much harder to see why we should play a mixed strategy in a one-shot game.