# Distilling Bayesian Belief States into Language Models for Auditable Negotiation

arXiv: https://arxiv.org/abs/2605.04507 · HTML: https://mlsanity.com/paper/2605.04507/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 11 references that are in the map.
- First posted on arXiv 6 May 2026.

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

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Deal or No Deal? End-to-End Learning for Negotiation Dialogues](https://mlsanity.com/paper/1706.05125/) (2017)
- [Cooperation, Competition, and Maliciousness: LLM-Stakeholders Interactive Negotiation](https://mlsanity.com/paper/2309.17234/) (2023)
- [CaSiNo: A Corpus of Campsite Negotiation Dialogues for Automatic Negotiation Systems](https://mlsanity.com/paper/2103.15721/) (2021)
- [Opponent Modeling in Negotiation Dialogues by Related Data Adaptation](https://mlsanity.com/paper/2205.00344/) (2022)
- [Multi-Issue Bargaining With Deep Reinforcement Learning](https://mlsanity.com/paper/2002.07788/) (2020)
- [BEDA: Belief Estimation as Probabilistic Constraints for Performing Strategic Dialogue Acts](https://mlsanity.com/paper/2512.24885/) (2025)

## Built on by (most cited first, 1 of 1)

- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)

## Abstract (arXiv)

Negotiation agents must infer what their counterpart values, update those beliefs over dialogue turns, and choose actions under uncertainty. End-to-end large language models (LLMs) can imitate negotiation dialogue, but their opponent beliefs are usually implicit and difficult to inspect. We propose BOND (Bayesian Opponent-belief Negotiation Distillation), a framework for auditable negotiation. BOND consists of an LLM-based Bayesian teacher that scores dialogue contexts against the six possible opponent priority orderings, updates a posterior over those orderings, and uses the posterior for menu-based decision making, as well as a smaller 8B student language model that emits both negotiation actions and normalized posterior beliefs as tagged text. In the CaSiNo negotiation dataset, BOND outperforms the state-of-the-art and achieves mean Brier score 0.085 over opponent-priority posteriors. The distilled student preserves much of this belief signal, achieving Brier 0.114, below the uniform six-ordering reference of 5/36, approximately 0.139. Compared with a 70B structured-CoT baseline, the significantly smaller 8B student model yields substantially better elicited posterior calibration. We further showcase auditability through posterior trajectories, belief-versus-policy error decomposition, and posterior-prefix interventions. These diagnostics reveal that distillation preserves a scoreable belief report more strongly than causal belief-conditioned control, making weak belief-action coupling visible, not hidden.