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.

翻译：信息设计研究发送者如何影响接收者的最优行为以实现特定目标。尽管信息设计源于日常人类交流，现有的博弈论与机器学习方法通常将信息结构建模为数值，这限制了许多应用只能停留在玩具博弈层面。本研究利用大语言模型，提出了贝叶斯劝说中的言语化框架，首次将经典贝叶斯劝说扩展至涉及人类对话的真实世界博弈。具体而言，我们将贝叶斯劝说映射为言语化调解者增强的扩展式博弈，其中大语言模型实例化发送者与接收者。为高效求解该言语化博弈，我们提出了一种结合大语言模型与博弈求解器的广义均衡寻找算法。该算法通过言语化承诺假设、言语化服从约束及信息模糊化等技术进行强化。在推荐信、法庭互动及执法等对话场景中的数值实验表明，我们的框架既能复现经典贝叶斯劝说的理论结果，也能在更复杂的自然语言与多阶段场景中发现有效的劝说策略。