Verbalized Bayesian Persuasion

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 information obfuscation. Numerical experiments in dialogue scenarios, such as recommendation letters, courtroom interactions, and law enforcement, validate that our framework can both reproduce theoretical results in classic BP and discover effective persuasion strategies in more complex natural language and multi-stage scenarios.