We consider a persuasion problem between a sender and a receiver where utility may be nonlinear in the latter’s 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). Because of 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 we illustrate our methodology by studying information sharing of waiting times in service systems翻译一下

我们考虑一个发件人和接收者之间的说服问题，其中接收者的效用可能在其信念中是非线性的；我们把这样的接收者称为风险感知者。这种效用模型出现在接收者偏离预期效用最大化的系统性偏差中，例如不确定性规避（例如，对于等待服务的等待时间方差的敏感性）。由于这种非线性，使用启示原则寻找最优说服机制的标准方法失败了。为了克服这个难点，我们利用问题的基本几何形状，开发了一个凸优化框架来找到最优的说服机制。我们定义了完全说服的概念，并使用我们的框架来表征实现完全说服的条件。我们使用我们的方法研究了二元说服问题，其中接收者有两个行动，发件人在每个状态下都严格偏好其中一个。在凸性假设下，我们证明了二元说服问题可以简化为线性规划，并建立了一个规范信号集，其中每个信号要么揭示状态，要么在接收者两个状态之间引起不确定性。最后，我们讨论了我们的方法对更一般情境的广泛适用性，并通过研究服务系统中等待时间的信息共享来说明我们的方法论。

相关问题

The literal interpretation of risk consciousness is that the agent’s behavior deviates systematically from expected utility maximization. Such deviations are well documented in the literature; we provide a few examples in Table 1 and discuss them in Online Appendix F. For instance, an agent with uncertainty aversion may be modeled using meanstandard deviation utility. Thus, there is a need to develop a theory for the persuasion of such agents, both to better capture realistic behavior in operational settings and to gain qualitative insights into phenomena that do not arise with EUM receivers.谈一下你对这段话的理解

这段话主要讨论了风险意识和行为偏差之间的关系。在现实生活和研究中，已经有很多例子表明，人们在面对风险时的行为往往不是简单的期望效用最大化，而是存在系统性的偏差。例如，有些人对不确定性有很强的厌恶，这种心理可以用均值-标准差效用来建模。因此，需要开发一种理论来说服这些具有风险意识的个体，以更好地捕捉操作环境中的现实行为，并获得有关EUM接收者不会出现的现象的定性洞察。

. Binary Persuasion这个词什么意思

Binary Persuasion是由两个词组成的术语。Binary 意味着 "由两个部分组成"，而 Persuasion 则意味着 "说服"。因此，Binary Persuasion就是通过两个方面来说服某人，或者通过两个不同的观点来达成某种共识或决策。这个词通常应用于营销和广告领域，意味着使用两个不同的方法来说服潜在消费者购买某个产品或服务。