Improving Cooperation in Language Games with Bayesian Inference and the Cognitive Hierarchy

TL;DR

The paper tackles robust cooperation in cooperative language games by addressing uncertainty in both semantics and pragmatics. It introduces a Bayesian framework that maintains a distribution over possible teammate language models and hierarchy levels, augmented with embedding perturbations to capture fine-grained semantic noise, and optimizes actions via a per-turn heuristic utility $E[U]$ guided by Bayesian updates. The approach is instantiated in Codenames with Bayesian spymaster and Bayesian guesser agents that learn from observations and leverage Monte Carlo estimates of $P(a\mid m)$ to adapt to teammates. Results show improved performance, especially against out-of-distribution teammates and under semantic uncertainty, suggesting practical impact for robust human–AI cooperation in language-based tasks.

Abstract

In two-player cooperative games, agents can play together effectively when they have accurate assumptions about how their teammate will behave, but may perform poorly when these assumptions are inaccurate. In language games, failure may be due to disagreement in the understanding of either the semantics or pragmatics of an utterance. We model coarse uncertainty in semantics using a prior distribution of language models and uncertainty in pragmatics using the cognitive hierarchy, combining the two aspects into a single prior distribution over possible partner types. Fine-grained uncertainty in semantics is modeled using noise that is added to the embeddings of words in the language. To handle all forms of uncertainty we construct agents that learn the behavior of their partner using Bayesian inference and use this information to maximize the expected value of a heuristic function. We test this approach by constructing Bayesian agents for the game of Codenames, and show that they perform better in experiments where semantics is uncertain