My PhD research was part of the project The Economics of Language, supervised by Robert van Rooij; Michael Franke worked on the same project. We investigated the use of game-theoretic and decision-theoretic models (taken originally from economics) to describe linguistic behaviour.
Earlier in the project I 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.
My thesis topic was 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 apply to Robert's project: game theory, decision theory and formal epistemology), and I tried to apply the models coming from that research field to formal semantics and pragmatics.
The dissertation is online, so you can see for yourself how successful I was.