AI 中文总结
针对委托人知晓代理人私人信息均值但不知其分布的模糊性授权问题，提出随机上限机制，证明其优于确定性上限，采用鞍点方法构造解，结果可扩展至凸序模糊性。
AI 中文摘要
在模糊性环境下，简单的授权规则是否最优？我们研究委托代理问题，其中委托人知晓代理人私人信息的均值，但不知其分布。在二次常偏差环境中，鲁棒最优的随机机制是随机上限（random cap）：委托人抽取并公布一个上限，代理人在此上限之下可自由选择。随机上限通过对冲针对特定上限的最坏情况分布，严格优于所有确定性上限。我们通过非递减且凹的期望行动规则刻画随机上限，并采用鞍点方法构造解。最坏情况分布在其连续区域具有指数生存函数，在上端点处有一个原子。在正则条件下，该结果可扩展至凸序模糊性。当均值低于代理人偏差时，最优机制还需要一个激励中性的结果彩票。
英文摘要
Are simple delegation rules optimal under ambiguity? We study delegation when the principal knows the mean, but not the distribution, of the agent's private information. In a parsimonious quadratic constant-bias environment, the robustly optimal randomized mechanism is a random cap: the principal draws and reveals an upper bound, below which the agent chooses freely. Randomization strictly outperforms every deterministic cap by hedging against cap-specific worst-case distributions. We characterize random caps through a nondecreasing and concave expected-action rule and construct the solution using a saddle-point approach. The worst-case distribution features an exponential survival function over its continuous region and an atom at the upper endpoint. Under regularity conditions, the result extends to convex-order ambiguity. Moreover, when the mean is below the agent's bias, an optimum can be implemented by supplementing the random cap with an incentive-neutral outcome lottery, while pure random caps are strictly suboptimal.
