An expected utility theory for state dependent preferences
This note is a generalization and improved interpretation of the main result of Karni and Schmeidler (An Expected utility theory for state dependent preferences. Working paper no. 48 80 of the Foerder Institute for Economic Research, Faculty of Social Sciences, Tel Aviv University, 1980) A decision maker is supposed to possess a preference relation on acts and another preference relation on state prize lotteries, both of which are assumed to satisfy the von Neumann Morgenstern axioms. In addition, the two preference relations restricted to a state of nature are assumed to agree. We show that these axioms are necessary and sufficient for the existence of subjective expected utility over acts with state dependent utility functions and a subjective probability measure. This subjective probability measure is unique when conditioned on the set of states of nature in which not all the prizes are equally desirable.