Ordinal, nonlinear context dependence

Prospect theory [KT79] and its more recent formalizations [KR06, KR07] prescribe "nonlinear" reference-dependence. The same may be said of other forms of context-dependence such as status quo bias [MO05]. Even in settings where there is a strong case for linear context-dependence such as Gilboa and Schmeidler's theory of case-based decisions, nonlinearity is typical in the absence of "diversity of preference". Furthermore, the hope of providing an axiomatic foundation for neuroscientific models of decision making, where context is interpreted as a physical state or "connectome" suggest a general, ordinal axiomatization of nonlinear context-dependence is called for. As with traditional, "context-free" models of ordinal utility (eg. Debreu [Deb54]), the issue of continuity is central: precise, yet simple and intuitive, conditions on the set of contexts are needed if preferences have a representation that is continuous across contexts. The continuity condition I employ is the obvious choice and is a generalisation of [GS03a]. There are interesting connections with literature on jointly continuous utility [Lev83, CCM09]. Finally, a promising feature of the present approach is it that may be used to axiomatise payoffs associated with discontinuous games (such as Bertrand oligopoly).