Agents receive private signals about an unknown state. The resulting joint belief distributions are complex and lack a simple characterization. Our key insight is that, when conditioned on the state, the structure of belief distributions simplifies: feasibility constrains only the marginal distributions of individual agents across states, with no joint constraints within a state. We apply this insight to multi-receiver persuasion, identifying new tractable cases and introducing optimal transportation and duality tools.

翻译：智能体接收关于未知状态的私有信号。由此产生的联合信念分布复杂且缺乏简单表征。我们的核心洞见在于，当以状态为条件时，信念分布的结构得以简化：可行性仅约束个体智能体在不同状态间的边缘分布，而在同一状态内部不存在联合约束。我们将这一洞见应用于多接收者说服模型，识别出新的可处理情形，并引入了最优传输与对偶工具。