Objective Lotteries as Ambiguous Objects: Allais, Ellsberg, and Hedging

Abstract

We derive axiomatically a model in which the Decision Maker can exhibit simultaneously both the Allais and the Ellsberg paradoxes in the standard setup of Anscombe and Aumann (1963). Using the notion of 'subjective', or 'outcome' mixture of Ghirardato et al. (2003), we define a novel form of hedging for objective lotteries, and introduce a novel axiom which is a generalized form of preferences for hedging. We show that this axiom, together with other standard ones, is equivalent to a represen- tation in which the agent reacts to ambiguity using multiple priors like the MaxMin Expected Utility model of Gilboa and Schmeidler (1989), generating an Ellsberg-like behavior, while at the same time, she treats also objective lotteries as 'ambiguous objects,' and use a fixed (and unique) set of priors to evaluate them – generating an Allais-like behavior. We show that this representation is equivalent to one in which the agent evaluates lotteries using a set of concave rank-dependent utility functionals. A comparative notion of preference for hedging is also introduced.

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