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 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. We map the BP to a verbalized mediator-augmented 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. Experiments in dialogue scenarios, such as recommendation letters, law enforcement, diplomacy with press, validate that our framework can reproduce theoretical results in classic BP and discover effective persuasion strategies in more complex natural language and multi-stage scenarios.