Second-order ambiguous beliefs
This paper provides an axiomatic characterization of ambiguous (= set valued) beliefs in the setting of a two-stage expected utility model. In an Anscombe-Aumann [\textit{F. J. Anscombe} and \textit{R. J. Aumann}, Ann. Math. Stat. 34, 199--205 (1963; Zbl 0114.07204)] setting but without reversal of order, and thus comparable to \textit{K. Seo}'s [Econometrica 77, No. 5, 1575--1605 (2009; Zbl 1178.91053)] characterization of two-stage expected utility, the paper characterizes (i) a representation that looks analogous to variational preferences, (ii) the special case in which the decision maker minimaxes over a set of second-stage beliefs, (iii) a further extension in which dropping the completeness axiom leads to an incomplete, ``multiple tastes'' preference (i.e., the preference relation is the intersection of many complete ones). The paper mostly speaks to theorists; a main contribution is to carefully elucidate how classic models like maxmin expected utility [\textit{I. Gilboa} and \textit{D. Schmeidler}, J. Math. Econ. 18, No. 2, 141--153 (1989; Zbl 0675.90012)] connect to the recent literature on two-stage expected utility. An instructive discussion of these connections is provided. The richness of the model, and a lack of uniqueness of second-stage beliefs, may limit the appeal of the paper's novel decision models to readers who have applications in mind.
scientific article; zbMATH DE number 6162239
scientific article