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For example, agent
b
may beliefs agent
a
prefer (
{
a, b, c
}
,movie
)to
(
{
a, b
}
,movie
), or formally
bel
b
((
{
a, b, c
}
,movie
)
a
(
{
a, b
}
,movie
))
(which happens to be incorrect in this case).
Intuitively, the goal of the game is to partition the set of agents into
a stable coalition structure of exhaustive and non-overlapping coali-
tions. We assume that the outcome of a coalition is decided only by
the coalition itself (i.e., who its members are) and the joint action cho-
sen. For this reason, we define a coalitional act by a couple
α
=(
C, a
),
where
C
A
, which represents the possible outcomes
achievable by the members of the coalition
C
performing the joint-
action
a
. For any two coalitional acts
α
1
=(
C
1
,a
1
)and
α
2
=(
C
2
,a
2
),
i
⊂
N
and
a
∈
∈
C
1
∩
C
2
,wehave
α
1
i
α
2
if agent
i
prefers
α
1
to
α
2
.
Example 4.8
The situation depicted in Example 4.2 can be for-
malised as a NTU-PB game
N,A,
(
i
)
,B
,inwhich:
•
N
=
{
John
,
Mary
}
.
•
A
=
Bonheur Restaurant, Sashimi Hiro, Jashan, Spasso, Domani,
Yung Kee
{
}
.
•
The following shows a full list of coalitional acts.
(
{
John
}
, Bonheur Restaurant
)
}
,
(
{
John
}
, Sashimi Hiro
)
}
,
(
{
John
}
, Jashan
)
}
,
(
{
John
}
, Spasso
)
}
,
(
{
John
}
, Domani
)
}
,
(
{
John
}
, Yung Kee
)
}
,
(
{
Mary
}
, Bonheur Restaurant
)
}
,
(
{
Mary
}
, Sashimi Hiro
)
}
,
(
{
Mary
}, Jashan
)
},
(
{
Mary
}, Spasso
)
},
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