How should an agent (the sender) observing multi-dimensional data (the state vector) persuade another agent to take the desired action? We show that it is always optimal for the sender to perform a (non-linear) dimension reduction by projecting the state vector onto a lower-dimensional object that we call the "optimal information manifold." We characterize geometric properties of this manifold and link them to the sender's preferences. Optimal policy splits information into "good" and "bad" components. When the sender's marginal utility is linear, revealing the full magnitude of good information is always optimal. In contrast, with concave marginal utility, optimal information design conceals the extreme realizations of good information and only reveals its direction (sign). We illustrate these effects by explicitly solving several multi-dimensional Bayesian persuasion problems.
翻译:观察多维数据( 状态矢量) 的代理( 发送者) 如何说服另一个代理( 状态矢量) 采取想要的行动? 我们显示, 发送者通过将状态矢量投射到一个我们称之为“ 最佳信息元数” 的低维对象上, 总是最理想的( 非线性) 递减维度 。 我们确定此多维的几何特性, 并将其与发送者偏好联系起来 。 最佳政策将信息分为“ 好” 和“ 坏” 元件 。 当发送者的边际功能是线性时, 显示好信息的全部大小总是最理想的 。 相反, 最佳信息设计通过连接边际功能, 隐藏好信息的极端认识, 并且只揭示其方向( 信号 ) 。 我们通过明确解决多个多维的巴耶斯说服问题来说明这些效果 。