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 pragmatically competent language agents.