We present data from three experiments addressing how much theory of mind reasoning is involved in production and interpretation of ambiguous referential expressions in an artificial language task, and how this interacts with the cost and availability of alternative utterances. When an unambiguous alternative is not available, listeners tend to draw simple Quantity inferences reminiscent of scalar implicatures (Grice, 1975). When an unambiguous alternative is available, fewer inferences are observed, but gradiently more as the cost of unambiguous alternatives increase. We outline a novel game theoretic model of pragmatic reasoning based on probabilistic back-and-forth reasoning about interlocutors’ rational choices and beliefs. The model provides a good fit to the data and raises interesting issues for future research.