The structure of variational preferences

Maccheroni, Marinacci, and Rustichini (2006), in an Anscombe-Aumann framework, axiomatically characterize preferencesthat are represented bythe variational utility functional V(f)=min_p∈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^{{star operator}} and d^{{star operator}}. The function c^{{star operator}}, also identified by Maccheroni, Marinacci, and Rustichini (2006), fully characterizes the decision maker's attitude toward uncertainty, while the novelfunction d^{{star operator}} characterizes the uncertainty perceivedby the decision maker.