Preferences with Changing Ambiguity Aversion

In this paper, we study two extensions of Gilboa and Schmeidler (1989)’s maxmin expected utility decision rule to accommodate a decision maker’s changing ambiguity attitude. The two rules are respectively a weighted maxmin rule and a variant constraint rule. The former evaluates an act by a weighted average of its worst and best possible expected utilities over a set of priors, with the weight on the worst case depending on the act. The latter evaluates an act by its worst expected utility over a neighborhood of a set of approximating priors, with the size of the neighborhood depending on the act. Canonical representations of the two rules are provided for classes of preferences that exhibit respectively ambiguity aversion of Schmeidler (1989) and ambiguity aversion of Ghirardato and Marinacci (2002). When restricted to the class of preferences exhibits both versions of ambiguity aversion, our results provide two alternative representations in addition to the ambiguity averse representation provided by Cerreia-Vioglio, Maccheroni, Marinacci and Montrucchio (2011). In the second part of this paper, we study the wealth effect under ambiguity. We propose axioms on absolute and relative ambiguity aversion and derive the three representations for the ambiguity averse preferences displaying decreasing (increasing) absolute ambiguity aversion. In particular, decreasing absolute ambiguity aversion implies that as baseline utility increases, a weighted maxmin decision maker puts less weight on the worst case, and a variant constraint decision maker considers a smaller neighborhood of approximating priors.