  We provide foundations for decisions in face of unlikely events by extending
the standard framework of Savage to include preferences indexed by a family of
events. We derive a subjective lexicographic expected utility representation
which allows for infinitely many lexicographically ordered levels of events and
for event-dependent attitudes toward risk. Our model thus provides foundations
for models in finance that rely on different attitudes toward risk (e.g.
Skiadas [9]) and for off-equilibrium reasonings in infinite dynamic games, thus
extending and generalizing the analysis in Blume, Brandenburger and Dekel [3].
