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{{
a
},{
b
},{
c
}}
2
3
4
{
b
}
{
b
},{c}
{
c
}
6
{
a
,
c
}
{{
a
,
b
},{
c
}}
{{
a
},{
b
,
c
}}
{{
a
,
c
},{
b
}}
{{
a
,
b
,
c
}}
Fig. 6.4
Raisable objections.
consistent with the external beliefs, we see that no coalition structure
is stable if both potential and definite objections are allowed by the
analysis (this can be seen by the fact that each node in Figure 6.3 has
at least one out-going solid or dashed edge). However, there are two
stable outcomes, namely
{{
a, b, c
}}
and
{{
a
}
,
{
b
}
,
{
c
}}
if only definite
objections are considered (Figure 6.5).
{{
a
},{
b
},{
c
}}
4
2
{
c
}
3
{
b
}
{
b
},{c}
5
{
a
,
b
}
{{
a
,
b
},{
c
}}
{{
a
},{
b
,
c
}}
{{
a
,
c
},{
b
}}
11
8
9
{
a
,
c
},{
b
}
{
a
,
b
},{
c
}
10
7
12
{
a
},{
b
,
c
}
{
a
,
b
,
c
}
{
a
,
b
,
c
}
{
a
,
b
,
c
}
{{
a
,
b
,
c
}}
Fig. 6.5
Definite objections.
Second, in cases where the agents do not raise any objections that
are inconsistent with their external beliefs, which is depicted in figure
6.4, we see that there is one stable outcome, namely
{{a}, {b}, {c}}
,if
both raisable potential objection and raisable definite objections are al-
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