Awareness-dependent subjective expected utility

We develop awareness-dependent subjective expected utility by taking unawareness structures introduced in Heifetz et al. (J Econ Theory 130:78–94, 2006; Games Econ Behav 62:304–324, 2008; Unawareness, beliefs, and speculative trade. University of California, Davis, 2011a) as primitives in the Anscombe–Aumann approach to subjective expected utility. We observe that a decision maker is unaware of an event if and only if her choices reveal that the event is “null” and the negation of the event is “null”. Moreover, we characterize “impersonal” expected utility that is behaviorally indistinguishable from awareness-dependent subject expected utility and assigns probability zero to some subsets of states that are not necessarily events. We discuss in what sense probability zero can model unawareness.