We consider a model of Bayesian persuasion with one informed sender and several uninformed receivers. The sender can affect receivers' beliefs via private signals, and the sender's objective depends on the combination of induced beliefs. We reduce the persuasion problem to the Monge-Kantorovich problem of optimal transportation. Using insights from optimal transportation theory, we identify several classes of multi-receiver problems that admit explicit solutions, get general structural results, derive a dual representation for the value, and generalize the celebrated concavification formula for the value to multi-receiver problems.

翻译：本文考虑一个包含一位知情发送者和多位不知情接收者的贝叶斯说服模型。发送者可通过私人信号影响接收者的信念，且发送者的目标取决于所诱导信念的组合。我们将说服问题简化为最优传输中的Monge-Kantorovich问题。利用最优传输理论的洞见，我们识别出多类可求得显式解的多接收者问题，获得一般性结构结果，推导出价值的对偶表征，并将经典的价值凹化公式推广至多接收者问题。