To formally describe the Ergin-Gul representation, note that exploiting the product
structure of the state space allows an act f to be represented as
where {A
1
,…,A
n
} is a partition of
S
a
,{B
1
,...,B
m
}
is a partition of
S
b
, and x
ij
is the
prize delivered by f at all states s∈A
i
×B
j
. Given a product measure μ=μ
a
×μ
b
on
S
, associate with f the two-stage compound lottery
Under Ergin and Gul’s axioms, there exists a unique product measure μ=μ
a
×
μ
b
on
S
such that every act f is evaluated according to W ( f(·)) =V
*
(P
f
*
), where P
f
*
is the compound lottery associated with f and V
*
is a suitably contin ...
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