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.

Persuasion shapes much of our daily life—from professors writing recommendation letters, to prosecutors arguing in court, to diplomats negotiating with allies. Economists estimate it drives nearly a quarter of all economic activity. For decades, researchers have studied how to craft messages that guide others' decisions, but their mathematical tools only worked in dramatically simplified settings. Classic theory might reduce a student's qualifications to just "strong" or "weak," losing all the nuance that real recommendation letters actually convey. This paper bridges that gap. We use large language models—the AI systems behind today's chatbots—to bring rigorous theories of persuasion into the real world of natural conversation. Instead of working with abstract numerical signals, our framework reasons about actual letters, courtroom arguments, and diplomatic messages, while still applying game theory to find effective communication strategies. We tested our approach across scenarios ranging from classic textbook examples to complex multi-round negotiations in the strategy game Diplomacy. Our framework reliably recovers known mathematical solutions on simple problems and discovers effective strategies in messy, language-rich situations. It even reveals human-like dynamics—such as senders initially being honest to build trust before strategically withholding information. This work opens new possibilities for studying persuasion in genuine human contexts, from political communication to fair information-sharing systems.