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sb-core. Thus we see that
is the most stable coalition
structure in this game as it is stable regardless of the agents' conflict
resolution strategies, followed by
{{
a
}
,
{
b
}
,
{
c
}}
which may be stable, but
is depend ent on the agents' conflict resolution strategy, followed by
the rest of the coalition structures which are certainly not stable.
{{
a, b, c
}}
6.4 Properties
The relationship among the four proposed belief based cores is interest-
ing. In the following theorem, we show that the wb-core is a superset
of the sb-core; the w-core is a superset of the s-core; the sb-core is
a superset of the s-core; and the wb-core is a superset of the w-core.
This is depicted in Figure 6.5.
6.4.1
Relationships of the four criteria
Theorem 6.1
The wb-core is a superset of the sb-core. Similarly,
the w-core is a superset of the s-core. The sb-core is a superset of the
s-core whereas the wb-core is a superset of the w-core. (Refer to Figure
6.7 for the complete picture).
Fig. 6.7
The four belief-based cores.
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