posterior preference relations. An observation, x, is essential if
(
a,b
)
≻
x
a
′
,b
′
, for some
(
a,b
)
,
a
′
,b
′
∈A×B
. Assume that all elements of
¯
X
are essential.
For every
a∈A
and
x∈
¯
X
, define a binary relation
x
a
on B as follows: for all
b
,b
′
∈B,b
x
a
b
′
if and only if
(
a,b
)
x
a,b
′
. An effect, θ, is said to be nonnull given
the observation–action pair
(
x,a
)
if
(
b
−θ
r)≻
x
a
b
−θ
r
′
, for some
b∈B
and
r,r
′
∈
R
; other-
wise, it is null given the observation–action pair
(
x,a
)
. Let Θ(a,x) denote the set of nonnull
effects given (x,a).
1.4.2 Preferences on Strategies and their Representation
Suppose that
on
I
is a continuous w ...
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