# Distilling Bayesian Belief States into Language Models for Auditable Negotiation Source: [Distilling Bayesian Belief States into Language Models for Auditable Negotiation]() Collection index: [llms.txt]() Data updated: 2026-05-08T05:00:04.262Z Authors: Zongqi Cui, Baihan Lin Published: 2026-05-06T05:25:21.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Partner Ordering Prediction on Deal-or-No-Deal cross-domain transfer n=1695 turn snapshots](): Partner Ordering Prediction; Deal-or-No-Deal cross-domain transfer n=1695 turn snapshots; Brier Score: 0.1166. - [Opponent modeling on CaSiNo (External)](): Opponent modeling; CaSiNo (External); EMA: 53.84. - [Opponent priority-ordering prediction on CaSiNo (5-fold CV)](): Opponent priority-ordering prediction; CaSiNo (5-fold CV); EMA: 53.84. - [Negotiation performance and belief calibration on CaSiNo native (held-out dialogues)](): Negotiation performance and belief calibration; CaSiNo native (held-out dialogues); Accept-F1: 0.908. - [Opponent priority-ordering prediction on CaSiNo (150-dialogue held-out split)](): Opponent priority-ordering prediction; CaSiNo (150-dialogue held-out split); EMA: not recorded. ## Original sources and implementation [Original paper]() [PDF]()