This thesis offers a general game theoretic model of language use and interpretation and applies it to linguistic pragmatics in the vein of Grice (1989). The model presented here —called the ibr model explains pragmatic phenomena, such as conversational implicatures, as arising from a sequence of iterated best responses: starting from the literal, semantic meaning as a psychologically salient attractor of attention, speaker and hearer initially compute the rational best responses to a literal use or interpretation of expressions; subsequently, agents continue computing best responses to best responses, for as long as this is reasonable and their cognitive resources permit.