Strategic Conversation (STAC) is a five year interdisciplinary project that aims to develop a new, formal and robust model of conversation, drawing from ideas in linguistics, philosophy, computer science and economics. The project brings a state of the art, linguistic theory of discourse interpretation together with a sophisticated view of agent interaction and strategic decision making, which uses elements of both game theory and logic. The result has been the development of a model that goes far beyond the cooperative models of conversations assumed in almost all work in linguistics and economics on conversation.