As AI systems take on collaborative roles, they must reason about shared goals and beliefs—not just generate fluent language. The Rational Speech Act (RSA) framework offers a principled approach to pragmatic reasoning, but existing extensions face challenges in scaling to multi-turn, collaborative scenarios. In this paper, we introduce Collaborative Rational Speech Act (CRSA), an information-theoretic (IT) extension of RSA that models multi-turn dialog by optimizing a gain function adapted from rate-distortion theory. This gain is an extension of the gain model that is maximized in the original RSA model but takes into account the scenario in which both agents in a conversation have private information and produce utterances conditioned on the dialog. We demonstrate the effectiveness of CRSA on referential games and template-based doctor–patient dialogs in the medical domain. Empirical results show that CRSA yields more consistent, interpretable, and collaborative behavior than existing baselines—paving the way for more pragmatic and socially aware language agents.