The Structure of Variational Preferences

Maccheroni, Marinacci, and Rustichini [17], in an Anscombe-Aumann framework, axiomatically characterize preferences that are represented by the variational utility functional V (f) = min p2 Z u (f) dp + c (p) 8f 2 F; where u is a utility function on outcomes and c is an index of uncertainty aversion. In this paper, for a given variational preference, we study the class C of functions c that represent V . Inter alia, we show that this set is fully characterized by a minimal and a maximal element, c? and d?. The function c?, also identi?ed by Maccheroni, Marinacci, and Rustichini [17], fully characterizes the decision maker's attitude toward uncertainty, while the novel function d? characterizes the uncertainty perceived by the decision maker.