发表机构
Sophia University（上智大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在平滑模糊准则中，指数二阶期望效用是唯一能实现两层约简的函数形式，并刻画了其熵成本与对偶值的独特性质。
AI 中文摘要
指数二阶期望效用（SOEU）是模型不确定性的熵方法的基础。本文探讨了该函数形式在何种意义上是本质性的。在防误设的平滑模糊准则中，让单一参数同时控制模型层面的稳健性和跨模型的模糊厌恶聚合（Cerreia-Vioglio, Hansen, Maccheroni, and Marinacci, 2026）。那么，对于每个紧致模型集和每个二阶先验，该两层准则等于指数SOEU，并以贝叶斯预测测度为基线。主要结果是逆命题。在聚合器方面，匹配的曲率是必要的：在固定曲率下，没有其他连续、严格递增的聚合器能实现该约简，而在曲率不匹配时，存在一个模型集和一个先验，使得任何曲率和任何基线下的单层熵值都无法重现该准则。在成本方面，在包含卡方和逆Kullback-Leibler（KL）的幂散度族中，只有KL具有log-sum-exp形式的对偶，其他成员在第三累积量处首先偏离该形式。最后，与指数SOEU对偶的值是一个稳健控制值：它受理性疏忽的启发，但不存在关于固定行为的贝叶斯可行信息获取问题能产生它。
英文摘要
Exponential Second-Order Expected Utility (SOEU) underlies the entropic approach to model uncertainty. This paper explores in what sense that functional form is essential. In the misspecification-robust Smooth Ambiguity criterion, let a single parameter govern both the model-level robustness and the ambiguity-averse aggregation across models Cerreia-Vioglio, Hansen, Maccheroni, and Marinacci (2026). The two-layer criterion then equals Exponential SOEU for every compact set of models and every second-order prior, with the Bayesian predictive measure as the baseline. The main results are converses. On the aggregator side, matched curvature is \emph{necessary}: at a fixed curvature no other continuous, strictly increasing aggregator delivers the reduction, and with mismatched curvature there are a model set and a prior for which no single-layer entropic value, at any curvature and any baseline, reproduces the criterion. On the cost side, within the power-divergence family, which contains chi-squared and reverse Kullback--Leibler (KL), only KL has a dual of the log-sum-exp form, and the other members first depart from it at the third cumulant. Finally, the value dual to Exponential SOEU is a robust-control value: it is motivated by Rational Inattention, but no Bayes-plausible information-acquisition problem about a fixed act generates it.
