Information Technology Reference
In-Depth Information
the agents' preferences in Table 3.1, we must not have
x
1
,{s
∗
}
x
.
Hence
o
1
cannot be tennis. By the same token, it can be proved
that
o
2
,
o
3
,and
o
4
cannot be tennis. Therefore
x
does not exist
and
x
is in the core. Actually, it follows that the core is a singleton
{
(movie
,
movie
,
movie
,
movie)
}
.
It should be noted that even if the core is non-empty, it does not
necessary mean that the grand coalition
N
is stable. In the scenario
depicted in Example 3.17, although the core contains the consequence
{
, it does not guarantee that the grand
coalition
N
will be stable if the prevailing state
s
∗
= Good is not a
common knowledge. For example, if agent
A
4
,accordingtohisown
limited experience, concludes that the quality of the movie is bad, then
the grand coalition is not attractive to him, and agent
A
4
will prefer
to go to a tennis club to play tennis with someone else. Intuitively, we
will agent
A
4
has made a decision based on his 'incorrect belief'. More
precisely, agent
A
4
in this situation has got an experience so limited
that he forms an opinion
B
4
=
(movie
,
movie
,
movie
,
movie)
}
about the quality of the movie,
which, unfortunately, is inconsistent with the prevailing state, which
in turn causes
A
4
nottoprefertoseethemovie.
{
Bad
}
Example 3.18
We consider again the scenario in Section 3.2 and its
formal formulation in Example 3.5. Assume that the prevailing state is
s
∗
= Average instead. Intuitively, in this case agents
A
3
and
A
4
would
prefer playing tennis, hence the grand coalition with consequence
x
=(movie
,
movie
,
movie
,
movie)
is no longer stable. Formally, we say that in this case
x
=(movie
,
movie
,
movie
,
movie)
is not in the course. To show that this is the case, consider
C
=
{
3
,
4
}.
Search WWH ::
Custom Search