Nate Meyvis

Why don't people talk about the Shapley value more?

Here's an argument that the Shapley value is underrated:

  1. It's really important to figure out how to divide credit for the performance of a whole to the parts of that whole.
  2. The Shapley value is, under pretty mild constraints, the uniquely best way to do that.
  3. Those "mild constraints" really are pretty mild.
  4. Yet people barely talk about it.

I think that last assertion is pretty obvious, but in case you want evidence, here is a Marginal Revolution search for "Shapley." Its few results are mostly coverage of a Nobel Prize and Shapley's death. There is no direct application of the Shapley value (the closest thing is some mentions of the Gale-Shapley algorithm, again mostly in the form of Nobel coverage).

You might think that Shapley valuation is too much of an idealization to be useful. But I don't see how the Shapley value is worse in this regard than any number of other widely used and discussed tools from economics. In many respects it's better! (Again, because of the strength of the underlying uniqueness theorem.)

Here is an episode of My Favorite Theorem (a good podcast!) where Anil Venkatesh discusses the Shapley value and its many applications, including to the valuation of power-ups in video games.

There seems to be some use of the Shapley value in evaluating machine learning models (here is a blog post I find useful; a YouTube search will also turn up results).

Why isn't there a lot more of this? Why can't you, e.g., evaluate results in baseball games by considering observed results (of pitches, games, or whatever) as results of coalitions, and trying to determine Shapley values correspondingly?

My view of baseball researchers is that they'll try to apply any quantitative technique to baseball. My view of Tyler Cowen is that he'll apply any useful model, certainly over many years of blogging and speaking. What is going on here? Am I missing some fatal flaw in the Shapley value?

Published 2022-07-14.