My PhD research is part of the project The Economics of Language, supervised by Robert van Rooij; Michael Franke works on the same project. We investigate the use of game-theoretic and decision-theoretic models (taken originally from economics) to describe linguistic behaviour.
My thesis topic is unawareness of possibilities, and how we take account of it in natural dialogue. For instance you might ask me "Did you think of taking the bus?", not because you think it's necessarily the best idea but just to make sure that I haven't overlooked the possibility.
This idea has been around in linguistics for a long time, but so far as I know it hasn't had any serious formal treatment. Unawareness models are the New Hot Thing in economics (at least the kind of economics that I get to see: game theory, decision theory and formal epistemology), and I'm trying to apply the models that are coming out of that research to formal semantics and pragmatics.
For a preliminary stab at the problem see this draft (joint work with Michael Franke). It's oriented at decision theory (mainly because of the audience it's written for), but it descibes the kind of unawareness we're interested in and how it applies to language.
Previously in the project I've looked at game-theoretic explanations for implicature and at the division of labour between semantics and pragmatics; you can find a few efforts in those directions on the Publications page.