
Ambiguity and Ambiguity Aversion
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second-order utility ϕ(·) is concave if and only if the individual is smooth ambiguity averse,
in the sense that for every support K with associated second-order measure M, and for
every act f, the individual prefers the prize x
f
(M) to f — formally, x
f
(M)
K
f. A similar
construction can be used to characterize comparative smooth ambiguity aversion.
It should be noted that, due to the way x
f
(M) is defined, smooth ambiguity aversion
depends crucially on the representation of second-order preferences. Thus, the qualifica-
tions on second-order preferences, and on the interpretation of the smooth representa ...