Characterizations of Smooth Ambiguity Based on Continuous and Discrete Data
在Anscombe-Aumann框架下，研究了观测数据与平滑模糊偏好模型的一致性条件，揭示了该模型与复分析和泛函分析中经典数学结果之间的意外联系。
In the Anscombe-Aumann setup, we provide conditions for a collection of observations to be consistent with a well-known class of smooth ambiguity preferences (Klibanoff P, Marinacci M, Mukerji S (2005) A smooth model of decision making under ambiguity. Econometrica 73(6):1849–1892.). Each observation is assumed to take the form of an equivalence between an uncertain act and a certain outcome. We provide three results that describe these conditions for data sets of different cardinality. Our findings uncover surprising links between the smooth ambiguity model and classic mathematical results in complex and functional analysis.