A mathematical theory of cooperative communication

TL;DR

This paper introduces a mathematical framework for cooperative communication based on optimal transport theory, explaining how effective belief transmission occurs and its limitations, with implications for human cognition and human-robot interaction.

Contribution

It develops a novel mathematical model connecting cooperative communication to optimal transport, providing theoretical insights and computational validation of belief transfer mechanisms.

Findings

Proves cooperative communication enables robust belief transmission.

Shows the model explains human learning and interaction behaviors.

Demonstrates the framework's applicability through simulations.

Abstract

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.