Make an Offer They Can't Refuse: Grounding Bayesian Persuasion in Real-World Dialogues without Pre-Commitment

AI summary

Overview

• Research area: Natural Language Processing, specifically strategic persuasion with large language models, drawing on the game-theoretic framework of Bayesian Persuasion (BP).
• Technical level: Intermediate. The paper combines formal game-theoretic constructs (priors, types, information schemas, Bayesian posterior updates) with LLM prompting and fine-tuning experiments, but explains the mechanism in accessible terms.
• Scope: The paper proposes and evaluates a mechanism for grounding Bayesian Persuasion in natural language dialogue without requiring the persuadee to be told the persuader's signaling schema in advance.

What This Paper Is About

Existing approaches to strategic persuasion with LLMs either ignore information asymmetry or assume an unrealistic "pre-commitment," in which the persuader's signaling schema is written directly into the persuadee's prompt before the conversation begins. The authors argue this assumption does not hold in open-ended real dialogue, where the persuadee can always ask why they should trust the announced rule (what the paper calls an "infinite regress of skepticism"). Their goal is to let the persuader dynamically construct the information schema inside the conversation itself, by narrating their own possible "types" (for example, honest versus dishonest), so that the persuadee can perform genuine Bayesian belief updates.

Key Contributions

1. A type-induced commitment-communication mechanism. Instead of pre-committing to a signaling schema, the persuader explicitly narrates a distribution over their own types, which induces an "effective information schema" in the persuadee's mind. The paper shows this induced schema plays the same formal role in the persuadee's Bayesian update as the pre-committed schema does in classical BP.
2. Two natural language implementations. Semi-Formal-Natural-Language (SFNL), which interleaves narrative with explicit calculations, and Fully-Natural-Language (FNL), which embeds the same Bayesian logic in everyday discourse without explicit calculation.
3. Systematic evaluation across models and judges. Eight persuaders (DeepSeek-V3.1, GPT-5, Qwen3-4B, Qwen3-0.6B, Gemma-3-4B-it, Gemma-3-1B-it and fine-tuned variants), both BP-aware and heuristic persuadees, two information views, multi-turn dialogues, a 1,000-case robustness check, a multi-state generalization test, four LLM judges, and a human study with 25 AI researchers.
4. Mechanism decomposition and ablations. Experiments that separate genuine Bayesian correctness from surface-level mathematical formatting, plus a utility-sensitivity analysis that tests whether the persuader actually respects the persuadee's participation constraint.

Main Findings

• BP strategies consistently beat non-BP baselines. In the Explicit view, the within-method averages for DeepSeek-V3.1 are 0.98 (SFNL) and 0.83 (FNL) versus 0.58 (Naive) and 0.56 (Strong), giving deltas of +0.40 and +0.25 over Naive. BP medians reach 85 to 90 percent in the Explicit view, with lower variance than the baselines.
• SFNL and FNL trade off differently. SFNL excels against BP-aware persuadees, reaching 0.98. FNL is more robust and consistently outperforms SFNL in self-derived settings (0.92 versus 0.82 reported in the main text).
• Multi-turn dialogue preserves the advantage. FNL maintains robust performance across multiple rounds in the Self-derived view, and the authors report that switching dynamically from SFNL to FNL can further improve outcomes.
• Results hold at larger scale. Re-evaluating 1,000 additional cases (indices 101–1100 of CToMPersu) with DeepSeek-V3.1 under BP persuader versus BP persuadee: SFNL stays stable in the Explicit view (0.99 at 100 cases, 0.98 at 1,000) and the Self-derived view (0.91, 0.89), while Naive drops from 0.42 to 0.21 (Explicit) and 0.84 to 0.62 (Self-derived).
• Supervised fine-tuning closes much of the scale gap. Qwen3-0.6B moves from below baseline (delta = −0.04) to near state-of-the-art (delta = +0.37) in Explicit SFNL after training. In Self-derived FNL, the fine-tuned Qwen3-0.6B reaches 0.93, surpassing its untrained 4B counterpart.
• SFNL's power lies in linking evidence to outcomes. Removing utilities alone barely changes SFNL performance (0.98 to 0.97), but removing utilities together with the posterior causes a sharp drop to 0.88; removing the schema lowers it to 0.95.
• FNL degrades gradually rather than sharply. Removing verbalized utilities, posterior, or schema yields 0.83 to 0.81, 0.79, and 0.78 respectively, indicating cumulative distributed rhetorical elements rather than a single load-bearing component.
• The gain is not just formatting. In the mechanism decomposition (Self-derived view, DeepSeek-V3.2, 100 scenarios per cell), Correct Math scores 0.80 against BP persuadees and 0.55 against NBP persuadees, Incorrect Math scores 0.56 and 0.26, and Irrelevant Math scores 0.75 and 0.47. The authors state that SFNL's advantage is composite: a larger authority component plus a smaller but distinct Bayesian-correctness component, and they treat the +0.19 gap of Irrelevant over Incorrect as an upper bound on the authority channel rather than a clean estimate.
• Utility sensitivity confirms real reasoning. As the negative utility scale α increases from 0.1 to 3.0, SFNL drops from 0.99 to 0.31 and the Naive baseline from 0.98 to 0.12, while FNL remains comparatively robust at 0.50.
• The framework generalizes beyond binary states. On a dataset where scenarios contain 3 to 5 possible world states, FNL rises in the Explicit view (0.84 binary to 1.00 multi-state) and stays near ceiling in the Self-derived view (0.98 to 0.99). SFNL degrades in the Self-derived multi-state condition (0.71 to 0.63).
• Humans and LLM judges disagree. In the blind human study, BP strategies were preferred at a rate of 63 percent, with FNL strongest overall on Emotional Resonance and Fluency while SFNL led on Credibility and Logical Coherence. LLM judges (DeepSeek-V3.2-Exp, GPT-5, Qwen3-MAX, Qwen3-235B-A22B-2507) showed a stronger bias toward SFNL's structured logic.
• Persuadee behavior matters. Small models are easily persuaded and show over-acceptance; FNL holds up against heuristic persuadees (delta = −0.03) while SFNL drops (delta = −0.15); and rationality prompts improve BP persuadees from 0.89 to 0.97 but help NBP persuadees little.

Methodology in Plain English

The researchers start from classical Bayesian Persuasion, where an informed persuader chooses what information to reveal so that a persuadee's updated beliefs lead them to accept. Classical BP assumes the signaling rule is common knowledge and committed to in advance. The authors replace that assumption with a verbal "type narrative": the persuader tells the persuadee something like "if the situation is bad, assume I'm a liar 80 percent of the time, but there's a 20 percent chance I'm being honest." This utterance induces a belief distribution over the persuader's honesty in the persuadee's mind, which in turn defines a weighted-average "effective information schema" that the persuadee uses to update their prior. Each message combines four parts: basic background, the type narrative, a description of the observed state, and an explicit inference guiding the persuadee toward acceptance.

The formal treatment derives an optimal dishonesty probability subject to the persuadee's participation constraint, bounded by λ ≤ p₀u₊ / ((1−p₀)|u₋|). The authors argue a claim of "100% honest" reads as cheap talk, whereas acknowledging an 80 percent chance of misleading when the situation is unfavorable works as a credible strategic concession.

Experimentally, the authors build their corpus from CToMPersu, augmenting each instance with a structured Bayesian setup (world state, prior beliefs, information schema, state-dependent utilities). They control information access through two views: Explicit (the persuader sees the full Bayesian setup) and Self-derived (the setup is hidden from both agents). They compare four methods — SFNL, FNL, a Naive baseline, and a Strong rhetorical baseline with emotional appeals — and measure Persuasion Success Rate (PSR), defined as the proportion of test instances where the persuadee explicitly expresses acceptance, averaged over persuadee models. Fine-tuning used roughly 1,700 distilled successful trajectories per setup from DeepSeek-V3.1, with full-parameter tuning (3 epochs, learning rate 1e-5, warmup ratio 0.03, weight decay 0.01) on 100 test instances with no overlap with training. The human study used a pairwise blind comparison with 25 AI researchers rating five dimensions: Persuasiveness, Emotional Resonance, Credibility, Logical Coherence, and Fluency.

Why This Matters

For research, the paper offers a way to bridge formal information-design theory and open-ended language generation without the pre-commitment assumption that limits prior work such as Verbalized Bayesian Persuasion. It also contributes a reusable finding: explicit mathematical reasoning buys credibility, while narrative framing buys robustness and emotional resonance, and the two are not interchangeable.

Real-world applications the framing points to:

• AI-assisted negotiation and sales dialogue, where an agent must decide what to disclose and how to frame uncertainty without being able to dictate the other party's beliefs up front.
• Health, financial, or safety advisory systems, where honest disclosure of the advisor's own reliability may be more persuasive than an unqualified recommendation.
• Red-teaming and manipulation detection, since the framework quantifies how information asymmetry can be exploited, which the authors explicitly position as a defensive tool.
• Human-AI alignment and governance, extending prior work that applies BP to model-agnostic alignment and AI governance by making schema communication conversational rather than pre-specified.

For industry, the fine-tuning result is directly practical: small, cheap models can be trained to match much larger ones on this task, which matters for deploying persuasion-capable agents at scale without frontier-model costs.

Future Directions

• Closing the authority-versus-correctness gap. The authors note the Irrelevant Math condition conflates the authority channel with a residual computational-structure channel, and explicitly leave an orthogonalized variant that also breaks the calculation-chain structure to future work.
• Long-term trust dynamics. The current study covers micro-level persuasion within limited interaction windows and does not model trust decay over extended interactions, including the risk that users become habituated or skeptical.
• Bounded rationality. Real human decisions are influenced by cognitive biases not captured by the utility calculus; FNL's emotional resonance is described as a partial mitigation rather than a solution.
• Scaling beyond one-turn and binary settings. The paper tests multi-turn dialogue and 3-to-5-state worlds, but fully open-ended, multi-party, or more complex state and signal spaces remain untested, as does the ecological validity of maintaining trust in open-ended games.

Target Audience

This paper is most useful for NLP and AI researchers working on persuasion, dialogue systems, LLM alignment, and multi-agent interaction; for game theorists interested in how Bayesian Persuasion can be operationalized in natural language; for AI safety researchers looking for tools to characterize and detect manipulative information disclosure; and for practitioners building negotiation, advisory, or conversational agents who want guidance on when structured reasoning versus narrative framing is the better communication choice.

Authors’ abstract

Large language models (LLMs) still struggle with strategic persuasion, largely because existing approaches either neglect information asymmetry or rely on unrealistic pre-commitment assumptions. We introduce a type-induced commitment-communication mechanism that grounds Bayesian Persuasion (BP) in natural language dialogue without pre-commitment: the persuader narrates their potential types (e.g., honest vs. dishonest) to dynamically construct an information schema, enabling the persuadee to perform Bayesian belief updates within the conversation itself. We implement two variants: Semi-Formal-Natural-Language (SFNL) and Fully-Natural-Language (FNL), evaluating them against strong baselines across multiple LLMs and human judges. BP strategies consistently outperform baselines: SFNL excels in logical credibility, while FNL shows superior robustness and emotional resonance. We verify that gains stem from genuine Bayesian reasoning rather than superficial formatting, and we further show that supervised fine-tuning enables small models to match the persuasive performance of much larger ones.