Preferences with changing ambiguity aversion

We provide two extensions of Gilboa and Schmeidler (J Math Econ 18:141–153, 1989)’s maxmin expected utility decision rule to accommodate a decision maker’s changing ambiguity attitudes. 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 weights 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 preference relations that exhibit, respectively, ambiguity aversion à la Schmeidler (Econometrica 57:571–587, 1989) and ambiguity aversion à la Ghirardato and Marinacci (J Econ Theory 102:251–289, 2002). In the second part of this paper, we study wealth effect under ambiguity. We propose axioms on absolute and relative ambiguity aversion and derive three representations for the ambiguity averse preference relations exhibiting decreasing (increasing) absolute ambiguity aversion. In particular, decreasing absolute ambiguity aversion implies that as the baseline utility of an act 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.