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

arXiv: https://arxiv.org/abs/2412.12409 · HTML: https://mlsanity.com/paper/2412.12409/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 36 references that are in the map.
- First posted on arXiv 16 Dec 2024.

## Builds on (most cited first, 7 of 7)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [Advances in Pre-Training Distributed Word Representations](https://mlsanity.com/paper/1712.09405/) (2017)
- [GameBench: Evaluating Strategic Reasoning Abilities of LLM Agents](https://mlsanity.com/paper/2406.06613/) (2024)
- [Bayesian Action Decoder for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1811.01458/) (2018)
- [K-level Reasoning for Zero-Shot Coordination in Hanabi](https://mlsanity.com/paper/2207.07166/) (2022)
- [Learning to Perturb Word Embeddings for Out-of-distribution QA](https://mlsanity.com/paper/2105.02692/) (2021)

## Built on by (most cited first, 4 of 4)

- [Position: Theory of Mind Benchmarks are Broken for Large Language Models](https://mlsanity.com/paper/2412.19726/) (2024)
- [Shall We Play a Game? Language Models for Open-ended Wargames](https://mlsanity.com/paper/2509.17192/) (2025)
- [Decentralized Aggregation of LLM Predictions via Wagering Mechanisms](https://mlsanity.com/paper/2607.04389/) (2026)
- [Robust Is Salient: An Informed Adversary Moves the Optimal Signal onto the Salience Pole](https://mlsanity.com/paper/2610.00233/) (2026)

## Abstract (arXiv)

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