The structure of variational preferences

Maccheroni, Marinacci, and Rustichini (2006), in an Anscombe-Aumann framework, axiomatically characterize preferences that are represented by the variational utility functional V(f)=minp∈Δ{∫u(f)dp+c(p)}∀f∈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 identified by Maccheroni, Marinacci, and Rustichini (2006), fully characterizes the decision maker's attitude toward uncertainty, while the novel function d⋆ characterizes the uncertainty perceived by the decision maker.