Here’s an introduction to game theory. It highlights the lack of affinity between games and human action in the world.
Mises makes the same point in human action, pp. 115-117.
Here are a few articles on game theory and Austrian economics.
As far as I know, Rothbard did not endorse game theory. In fact, he solicited a critique of game theory for a lecture at an early 1990s Mises University.
Here is Lucas Engelhardt’s talk on Game Theory at Mises University last summer.