Incomplete Menu Preference and Ambiguity

This paper studies a problem of choice under uncertainty in which a decision-maker's (DM) choices randomly map to consumption outcomes. The primitive is a binary relation on menus, where a menu is a set of possible ex post outcomes. After the DM selects a menu, nature (not the DM) makes a consumption choice from the menu. Nature's choice function is subject to uncertainty, so that the choice of a particular menu yields a distribution over the ex post outcomes supported by that menu. Hence, from the DM’s view, by choosing a menu it is as if he is choosing a distribution over ex post outcomes. The main result provides axiomatic foundations for a menu-choice analogue of the Bewley model of Knightian uncertainty