I have been mulling Brian Weatherson's interesting reflections on why it is so hard to reduce game theory to decision theory. As Brian rightly notes much of decision theory doesn't get off the ground without the probabilities of possible outcomes. (As some of my regular readers on economics know this relates to my embrace of genuine Knightian uncertainty and informs my hostility to philosophers' fondness for decision theory.) But, as Brian points out, game theory is not like that. Now what I found particularly interesting is how Brian frames game theory as a species of epistemology. (He is not the first to do so, but for some reason his remarks hit home.) The key insight (among lots of fascinating ideas) is Brian's observation that "what we’re trying to do here is solve for what rationality requires the players credences to be, given some relatively weak looking constraints." If I understand Brian correctly, game theory becomes a kind of discovery mechanism (of these credences) given certain constraints and assumptions.
Now, I tend to think of these (rationality) assumptions, however minimal, as a normative ideal that is, in fact, only instantiated under rather rare social institutions. This is no reason for despair. It means that game theory can be a wider epistemic tool, even in the context of multiple equilibria, or none. For once we can specify what the credences would have been under ideal conditions, deviations from the norm may also be informative if, that is, we have a way of thinking about social causes. What I hope to do in the future is connect this tentative suggestions to some of the very interesting studies (including those by philosophers like Anna Alexandrova, Till Grüne-Yanoff, and Francesco Guala) on the application of game theory in the engineering of policy.
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