Questions of the type "What do you think other people would think?" For a study in the adoption of new technology, a student and I are developing a questionnaire that will poll domain experts on their opinions of what their colleagues would think about benefits/drawbacks of adopting a particular technology. This is research in social science/business but not strictly game theory, and as we are not economists, we don't know the literature.

Have economists/game theorists investigated questions of the type What do you think other people would think? If several experts can, say, draw technology acceptance distribution functions that reflect their own beliefs about the community's attitude toward a particular strength or weakness of a new technology, then the geometrical average of those distribution functions could be a starting point for inquiry into ranking the relative importance of a set of several strengths and weaknesses. Has this been done before? By whom?

We are not asking for a tutorial here, just a pointer to where should we should start looking for prior art.



Full disclosure: I asked this question on SE/Psychology and Neuroscience and did not receive meaningful answers.
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.