What Do Agents Think? How to Derive Revealed Ambiguity from Obviously Profitable Choices

Abstract

Starting from a general Bernullian complete preference relation, we study obviously profitable choices, i.e., rankings that constant acts can unambiguously mediate. Unlike the unambiguous choices studied in GMM, obviously profitable choices do not rely on contingent reasoning. Quite the opposite, the DM is completely agnostic about the real correlation structure between payoffs. Our first result is to show that obviously profitable choices admit a (symmetric) twofold multi-prior representation. After showing that an equivalent correlation-neglect Knightian representation is also available, we investigate whether a precise mathematical relationship exists between unambiguous and obviously profitable choices. In our main result, we show that obviously profitable choices identify the notion of revealed ambiguity put forward by GMM. This finding has two key implications. It shows that like GMM's unambiguous choices, obviously profitable choices are a valid alternative for identifying the collection of probabilistic scenarios the Decision Maker deems possible. It also illustrates how the Bewley model and the symmetric multi-prior model are dual to each other. A local analysis, similar to the one performed by Ghirardato and Siniscalchi (2012), further corroborates such duality.

Keywords: Revealed Ambiguity, Affine Core, Obvious Core, Confident Choices

JEL Classification: D80, D81