Questions of the type "What do you think other people would think?"
Epistemic game theory would be the closest (sub-)field that deals with questions involving higher order beliefs among interacting agents. 

The introductory article by Dekel and Siniscalchi is a good entry point to the literature. From its introduction:


  Epistemic game theory formalizes assumptions about rationality and mutual beliefs in a formal language, then studies their behavioral implications in games. Specifically, it asks: what do different notions of rationality and different assumptions about what players believe about ... what others believe about the rationality of players imply regarding play in a game?


"Epistemic Foundations of Game Theory" on the Stanford Encyclopedia of Philosophy has a less technical introduction. 

There is also a strand of literature in behavioral economics that studies cognitive hierarchies. The theories there are developed mostly to explain behaviors in the lab settings. Crawford, Costa-Gomes, and Iriberri (2013) provide a good summary.