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movie they are going to see, being also directed by Spielberg, should
be good. Also, according to their preference in Table 3.1, movie is pre-
ferred over tennis in this case. So if both agents make their decision
purely based on their experiences, the coalition should certainly be
stable unless
A
3
or
A
4
also prefer the movie (in which case
A
1
,say,
might prefer the movie watching coalition of
).
Similarly, any tennis playing coalition involving either
A
1
or
A
2
will
certainly fall apart as both agents have a better option according to
their beliefs.
However, a
{
A
1
,A
3
}
,to
{
A
1
,A
2
}
movie watching coalition is more prob-
lematic as there are conflicting entries in the viewing history of
A
3
and
A
4
.Inthiscase,both
A
3
and
A
4
are very likely to conclude from their
experiences that the quality of the current movie may either be 'good'
or 'average,' yet according to their preferences, both agents will stay
in the coalition only if the quality of the movie is good. Therefore the
stability of this coalition depends on how the conflicts are resolved by
these two agents. If both of them consider the movie quality to be
good, then the coalition is stable. Otherwise, the coalition is unstable
as agents
A
3
and
A
4
would rather play tennis instead. However, how
agents
A
3
and
A
4
are going to conclude on the quality of the movie is
unknown to the other two agents
A
1
and
A
2
.
Thus we see that the traditional core-based coalition stability con-
cepts, which classify all coalitions as either being in the core or not,
are insu
cient to describe games with uncertainty such as the one just
described. Instead, we need a new model that can classify coalitions
into different levels of stability. On one extreme, we have the certainly
stable coalitions such as the
{
A
1
,A
2
,A
3
,A
4
}
movie watching coalition. On the
other extreme, we have the certainly not stable coalition of
{
A
1
,A
2
}
A
1
,A
2
}
tennis playing coalition, and somewhere in between, we have the prob-
ably stable movie coalition of
{
.
The game discussed in the above example is typical example of a
type of games that we call
non-transferable utility games with inter-
nal uncertainty
(NTU-IU games). The adjective 'internal' refers to the
{
A
1
,A
2
,A
3
,A
4
}
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