We study a Bayesian persuasion problem where a sender wants to persuade a receiver to take a binary action, such as purchasing a product. The sender is informed about the (binary) state of the world, such as whether the quality of the product is high or low, but only has limited information about the receiver's beliefs and utilities. Motivated by customer surveys, user studies, and recent advances in generative AI, we allow the sender to learn more about the receiver by querying an oracle that simulates the receiver's behavior. After a fixed number of queries, the sender commits to a messaging policy and the receiver takes the action that maximizes her expected utility given the message she receives. We characterize the sender's optimal messaging policy given any distribution over receiver types. We then design a polynomial-time querying algorithm that optimizes the sender's expected utility in this Bayesian persuasion game. We also consider approximate oracles, more general query structures, and costly queries.

翻译：我们研究了一个贝叶斯劝导问题：发送方希望说服接收方采取二元行动（例如购买产品）。发送方了解世界（二元）状态（例如产品质量是高是低），但对接收方的信念和效用仅有有限信息。受客户调查、用户研究以及生成式人工智能最新进展的启发，我们允许发送方通过查询一个模拟接收方行为的预言机来进一步了解接收方。在固定次数的查询后，发送方承诺一个消息策略，接收方则根据所接收的消息采取最大化其期望效用的行动。我们针对任何接收方类型的分布，刻画了发送方的最优消息策略。随后，我们设计了一个多项式时间的查询算法，以优化该贝叶斯劝导博弈中发送方的期望效用。此外，我们还考虑了近似预言机、更通用的查询结构以及有成本查询的情形。