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Then for
g
2
,wehave
s-core(
g
2
)=
∅
,
w-core(
g
2
)=
{{{
a
}
,
{
b
}
,
{
c
}}}
,
wb-core(
g
2
)=
{{{
a
}
,
{
b
}
,
{
c
}}}
,
sb-core(
g
2
)=
{{{
a
}
,
{
b
}
,
{
c
}}}
,
which is in accordance to Theorem 6.2.
6.4.3
Effect of Accuracy
In this section, we shall discuss and analyse the effects of belief in-
accuracy on stability of coalitions. As we discuss in Section 4, the
main reason for the existence of belief based cores is the inaccuracy in
agents' beliefs, and there are different levels of inaccuracy in agents'
beliefs. For any two external beliefs
B
1
and
B
2
, in general one is more
accurate than the other.
Definition 6.12 (Accuracy Relation of External Beliefs)
Giv-
en two external belief relations
B
1
and
B
2
,wesay
B
1
is more accurate
than
B
2
, if for all
j ∈ N
, we have the followings:
•
If
B
1
(
x
y
) holds but
B
2
(
x
y
) does not hold, then
x
y
j
j
j
holds.
•
If
B
2
(
x
y
) holds but
B
1
(
x
y
) does not hold, then
x
y
j
j
j
does not hold.
•
If
B
1
(
x
j
y
) holds but
B
2
(
x
j
y
) does not hold, then
x
j
y
holds.
•
If
B
2
(
x
j
y
) holds but
B
1
(
x
j
y
) does not hold, then
x
j
y
does not hold.
The accuracy relation can be naturally extended to external belief
profiles.
Definition 6.13 (Accuracy Relation of External Beliefs Pro-
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