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 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 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 [17], fully characterizes the decision maker's attitude toward uncertainty, while the novel function d* characterizes the uncertainty perceived by the decision maker.