Verbalized Bayesian Persuasion
Wenhao Li, Yue Lin, Xiangfeng Wang, Bo Jin, Hongyuan Zha, and Baoxiang, Wang
TL;DR
This paper introduces a novel framework using large language models to verbalize Bayesian persuasion in real-world human dialogue scenarios, extending classic models to complex, multi-stage natural language interactions.
Contribution
It proposes a verbalized Bayesian persuasion framework with a new equilibrium-finding algorithm that incorporates LLMs, enabling application to real-world dialogue-based games.
Findings
Framework reproduces classic BP results
Discoveres effective persuasion strategies in complex dialogues
Validates in scenarios like recommendations and courtroom interactions
Abstract
Information design (ID) explores how a sender influence the optimal behavior of receivers to achieve specific objectives. While ID originates from everyday human communication, existing game-theoretic and machine learning methods often model information structures as numbers, which limits many applications to toy games. This work leverages LLMs and proposes a verbalized framework in Bayesian persuasion (BP), which extends classic BP to real-world games involving human dialogues for the first time. Specifically, we map the BP to a verbalized mediator-augmented extensive-form game, where LLMs instantiate the sender and receiver. To efficiently solve the verbalized game, we propose a generalized equilibrium-finding algorithm combining LLM and game solver. The algorithm is reinforced with techniques including verbalized commitment assumptions, verbalized obedience constraints, and…
Peer Reviews
Decision·ICLR 2026 Conference Withdrawn Submission
The paper tries to reconcile information design (ID) with BP beyond toy numeric signals to realistic dialogue settings. The MAG formulation and Prompt-PSRO reduction are coherent and leverage established game-theoretic tools while keeping LLMs in-the-loop via prompt search. The conditional prompt function idea for multi-stage persuasion is natural, effective, and well motivated. The empirical suite spans REL/COR/LAE and a demanding Diplomacy benchmark. Reported results indicate that VBP reproduc
The theoretical claim (epsilon-approx BCE/Bayes-Nash) rests on the MAG reduction and Prompt-PSRO approximations, but some core assumptions and proofs are missing as far as I can see; clearer main-text conditions and limitations would strengthen soundness. Measurement of lying/honesty and several scores relies on LLM-based evaluators--this is problematic, as it risks circularity and model-judge bias; more non-LLM or human-verified assessments would increase credibility and, in my view, these are
The topic is interesting, and using LLMs for game-theoretic problems is also an interesting direction. The paper is clearly written and well-structured.
I have some concerns about the strength of the contribution. The proposed framework converts a Bayesian persuasion problem into a verbalized version and then solves it with LLMs. I understand that in some real applications, beliefs cannot be explicitly expressed as distributions and that the persuasion process is done through natural language. But what is the advantage of the proposed method compared methods like directly predicting the agents' behaviors using a ML model and then solving it usin
The paper tackles a conceptually interesting and timely question: how to operationalize information design and persuasion in the natural language domain.
Unfortunately, the current presentation makes it very hard to assess the actual contribution or scientific soundness of the work. The paper is poorly written and often reads as a mix of buzzwords rather than a clear, well-defined technical contribution. * It is unclear what exact problem the paper is solving. Is the goal to compute optimal signaling schemes in language? To translate classical BP instances into a verbalized domain? Or to show that LLMs can approximate equilibria? None of these a
The paper tries to bridge theory and real-world settings in Bayesian persuasion by enabling settings in which sender-receiver communications happen through natural language. This direction is interesting and potentially impactful.
While I find the general research direction to be quite interesting, its realisation requires substantial improvement. In general, one problem is that the paper is not clear about what exactly is being shown and how. Many important steps are only explained by words, without any formal definition, thereby hiding many important details. This contributes to creating confusion when reading the paper. I don’t understand what is the goal of Section 3 and the set-up it introduces. Definition 3.1 se
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Taxonomy
TopicsOpinion Dynamics and Social Influence