We consider a persuasion problem between a sender and a receiver whose utility may be nonlinear in her belief; we call such receivers risk-conscious. Such utility models arise when the receiver exhibits systematic biases away from expected-utility-maximization, such as uncertainty aversion (e.g., from sensitivity to the variance of the waiting time for a service). Due to this nonlinearity, the standard approach to finding the optimal persuasion mechanism using revelation principle fails. To overcome this difficulty, we use the underlying geometry of the problem to develop a convex optimization framework to find the optimal persuasion mechanism. We define the notion of full persuasion and use our framework to characterize conditions under which full persuasion can be achieved. We use our approach to study binary persuasion, where the receiver has two actions and the sender strictly prefers one of them at every state. Under a convexity assumption, we show that the binary persuasion problem reduces to a linear program, and establish a canonical set of signals where each signal either reveals the state or induces in the receiver uncertainty between two states. Finally, we discuss the broader applicability of our methods to more general contexts, and illustrate our methodology by studying information sharing of waiting times in service systems.

翻译：我们考虑发送者与接收者之间的说服问题，其中接收者的效用可能对其信念呈非线性关系，我们将此类接收者称为风险意识主体。当接收者表现出偏离期望效用最大化的系统性偏差时（例如由服务等待时间方差敏感性引发的不确定性规避），便会产生此类效用模型。由于这种非线性特性，基于显示原理的标准最优说服机制设计方法失效。为克服这一困难，我们利用问题的潜在几何结构，构建了一个凸优化框架来求解最优说服机制。我们定义了“完全说服”的概念，并借助该框架刻画了实现完全说服的条件。我们运用该方法研究了二元说服问题——即接收者仅有两种行动选择，且发送者在任何状态下都严格偏好其中一种行动。在凸性假设下，我们证明二元说服问题可简化为线性规划，并建立了一组规范信号集，其中每个信号要么揭示真实状态，要么使接收者在两个状态间保持不确定性。最后，我们讨论了该方法在更广泛情境中的适用性，并通过研究服务系统中等待时间的信息共享来阐述我们的方法论。