Verbalized Bayesian Persuasion
This work addresses the limitation of existing information design methods in real-world applications by extending Bayesian persuasion to human dialogues, though it is incremental as it builds on classic game theory with LLM integration.
The authors tackled the problem of applying Bayesian persuasion to real-world human dialogues by proposing a verbalized framework that uses LLMs as sender and receiver, enabling effective persuasion strategies in complex natural language scenarios such as recommendation letters and courtroom interactions.
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.