A revealed preference theory for non-expected utility on "certain × uncertain" consumption pairs

In this paper we consider a two-period decision problem, where the feasible set is the set of "certain × uncertain" consumption pairs. That is, the decision-maker chooses (x, m) in a feasible set, where x is a certain first-period consumption and m is a random second-period consumption, a Borel probability measure on the set of real numbers. The purpose of this paper is to present revealed preference theory for non-expected utility on "certain × uncertain" consumption pairs. We present necessary and sufficient conditions for the data to be consistent with some non-expected utility functions.