I found this article on a website that has lots of good, interesting, articles. Here, they apply concepts of game theory to NFL play-calling. Good stuff -- with mentions about Nash Equilibrium and "A Beautiful Mind."
Previous research on the balance between running and passing in the NFL has largely missed the mark because it has focused on only half of the equation. Opposing defenses have been ignored. In this article, I'll illustrate how game theory can be applied to football play calling, and how it explains the balance between various strategies.