Characterizations of Smooth Ambiguity Based on Continuous and Discrete Data


Mathematics of Operations Research

février 2017, vol. 42, n°1, pp.167 - 178

Départements : Economie et Sciences de la décision

Mots clés : smooth ambiguity; variational preferences; revealed preference; completely monotone functions; Afriat inequalities; moment problem

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.