
Edi Karni
16
The second axiom, which is analogous to Savage’s P.5, requires that the decision
maker not be indifferent among all acts. Formally:
(A.5) (Nontriviality) There are acts h and
in H such that
.
Preference relations that have the structure depicted by the axioms (A.1)–(A.5) have
subjective expected utility representations.
Theorem1.6 (Anscombe and Aumann) Let
be a binary relation on H. Then
is
a weak-order satisfying Archimedean, independence, state independence and nontriviality if and
only if there exists a real-valued function, u, on X and a probability measure π on S such that
is represented by
Moreover, u is unique ...