Algorithmic Persuasion Through Simulation: Information Design in the Age of Generative AI

How can an informed sender persuade a receiver, having only limited information about the receiver's beliefs? Motivated by research showing generative AI can simulate economic agents, we initiate the study of information design with an oracle. We assume the sender can learn more about the receiver by querying this oracle, e.g., by simulating the receiver's behavior. Aside from AI motivations such as general-purpose Large Language Models (LLMs) and problem-specific machine learning models, alternate motivations include customer surveys and querying a small pool of live users. Specifically, we study Bayesian Persuasion where the sender has a second-order prior over the receiver's beliefs. After a fixed number of queries to an oracle to refine this prior, the sender commits to an information structure. Upon receiving the message, the receiver takes a payoff-relevant action maximizing her expected utility given her posterior beliefs. We design polynomial-time querying algorithms that optimize the sender's expected utility in this Bayesian Persuasion game. As a technical contribution, we show that queries form partitions of the space of receiver beliefs that can be used to quantify the sender's knowledge.