A mathematical theory of cooperative communication

Cooperative communication plays a central role in theories of human cognition, language, development, culture, and human-robot interaction. Prior models of cooperative communication are algorithmic in nature and do not shed light on why cooperation may yield effective belief transmission and what limitations may arise due to differences between beliefs of agents. Through a connection to the theory of optimal transport, we establishing a mathematical framework for cooperative communication. We derive prior models as special cases, statistical interpretations of belief transfer plans, and proofs of robustness and instability. Computational simulations support and elaborate our theoretical results, and demonstrate fit to human behavior. The results show that cooperative communication provably enables effective, robust belief transmission which is required to explain feats of human learning and improve human-machine interaction. Introduction Cooperative communication is invoked across language, cognitive development, cultural anthropology, and robotics to explain people's ability to effectively transmit information and accumulate knowledge. Theories claim that people have evolved a specialized ecological niche [Tomasello, 1999 , Boyd et al., 2011] and learning mechanisms [Csibra and Gergely, 2009 , Grice, 1975 , Sperber and Wilson, 1986] , which explain our abilities to learn and accumulate knowledge; however, we lack mathematical theories that would allow us analyze basic properties of cooperative communication between agents.