Verbalized Bayesian Persuasion

Wenhao Li, Yue Lin, Hongyuan Zha, Baoxiang Wang

Keywords: Large Language Models, Information Design, Bayesian Persuasion, Game Theory, Multiagent Systems

Abstract:

The study of information design explores how an information designer can influence the optimal behavior of players to achieve a specific objective through the strategic selection of the information provided.
This paper focuses on a case, Bayesian Persuasion (BP), where the information designer holds an informational advantage over only one player.
While information design originates from everyday human communication, traditional game-theoretic or multi-agent reinforcement learning methods often model information structures as discrete or continuous scalars or vectors, this approach fails to capture the nuances of natural language, significantly limiting their applicability in real-world scenarios.
By leveraging the powerful language understanding and generation capabilities of large language models (LLMs), this paper proposes a verbalized BP framework that extends classic BP to real-world games involving human dialogues for the first time.
Specifically, we map the classic BP to a verbalized mediator-augmented game, where LLMs instantiate the information designer and receiver.
To efficiently solve the game in the language space, we transform agents' policy optimization into prompt optimization and propose a generalized equilibrium-finding algorithm with a convergence guarantee.
Numerical experiments in realistic dialogue scenarios, such as recommendation letters, courtroom interactions, and law enforcement, validate that the VBP framework can reproduce theoretical results in classic settings and discover effective persuasion strategies in more complex natural language and multistage settings.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

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Submission Number: 8456