The tension between persuasion and privacy preservation is common in real-world settings. Online platforms should protect the privacy of web users whose data they collect, even as they seek to disclose information about these data to selling advertising spaces. Similarly, hospitals may share patient data to attract research investments with the obligation to preserve patients' privacy. To deal with these issues, we develop a framework to study Bayesian persuasion under differential privacy constraints, where the sender must design an optimal signaling scheme for persuasion while guaranteeing the privacy of each agent's private information in the database. To understand how privacy constraints affect information disclosure, we explore two perspectives within Bayesian persuasion: one views the mechanism as releasing a posterior about the private data, while the other views it as sending an action recommendation. The posterior-based formulation helps consider privacy-utility tradeoffs, quantifying how the tightness of privacy constraints impacts the sender's optimal utility. For any instance in a common utility function family and a wide range of privacy levels, a significant constant utility gap can be found between any two of the three conditions: $\epsilon$-differential privacy constraint, relaxation $(\epsilon,\delta)$-differential privacy constraint, and no privacy constraint. We further geometrically characterize optimal signaling schemes under different types of constraints ($\epsilon$-differential privacy, $(\epsilon,\delta)$-differential privacy and Renyi differential privacy), all of which can be seen as finding concave hulls in constrained posterior regions. Meanwhile, by taking the action-based view of persuasion, we provide polynomial-time algorithms for computing optimal differentially private signaling schemes, as long as a mild homogeneous condition is met.

翻译：说服与隐私保护之间的紧张关系在现实世界中普遍存在。在线平台应保护其所收集数据的网络用户的隐私，即便它们试图通过披露这些数据的信息来销售广告位。同样地，医院可能在有义务保护患者隐私的前提下共享患者数据以吸引研究投资。为解决这些问题，我们构建了一个研究差分隐私约束下贝叶斯说服的框架，其中发送者必须设计最优的信号机制进行说服，同时保证数据库中每个代理的私人信息的隐私。为理解隐私约束如何影响信息披露，我们从两个角度探讨贝叶斯说服：一种将机制视为发布关于私人数据的后验，另一种将其视为发送行动建议。基于后验的公式有助于考虑隐私-效用的权衡，量化隐私约束的严格程度如何影响发送者的最优效用。在一个常见效用函数族和广泛隐私水平范围内的任意实例中，ε-差分隐私约束、放松的(ε,δ)-差分隐私约束和无隐私约束这三种条件中的任意两者之间存在显著的恒定效用差距。我们进一步通过几何方法刻画了不同类型约束（ε-差分隐私、(ε,δ)-差分隐私和Renyi差分隐私）下的最优信号机制，所有这些均可视为在受限后验区域内寻找凹包。同时，通过采取基于行动的说服视角，我们提供了在温和的同质性条件下计算最优差分隐私信号机制的多项式时间算法。