Reference-dependent utility with shifting reference points and incomplete preferences

Many empirical studies have shown that people's preferences are reference-dependent. Previous theoretical studies of reference-dependence assumed that the reference point was fixed and then imposed the usual assumptions of decision theory, in particular completeness of preferences. This paper gives preference foundations for additive reference-dependent utility when the reference point varies across decisions and is one of the options in the decision maker's opportunity set. This decision situation is common, for example because usually the retention of the status quo is an available option, but is difficult to handle axiomatically because it implies incompleteness of preferences. The results of this paper provide tools to extend existing theories of reference-dependent preferences, such as prospect theory, to new and empirically important decision contexts.