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neither John nor Mary will raise the objection
{
(
{
John
,
Mary
}
, Yung Kee
)
}
.
For both John and Mary,
is
not
an objec-
tion, based on their private, incorrect, beliefs. As a result, the fact that
both dine at
Bonheur Restaurant
becomes a stable outcome, and the
coalitional act profile
{
(
{
John
,
Mary
}
, Yung Kee
)
}
becomes
a member in the b-core, even though they both genuinely consider
dining at
Yung Kee
is always a better alternative.
{
(
{
John
,
Mary
}
, Bonheur Restaurant
)
}
Example 4.17
It is worth noting that in Example 4.5, the coali-
tional act profile
{
(
{
John
,
Mary
}, Yung Kee
)
}
, being a member of the
core, is also in the b-core. This can be easily shown by following the
formal definition of b-core. In a nutshell, for the coalitional act pro-
file
, we are unable to find another coali-
tional act profile that genuinely dominates it, so we do not need to
bother whether it is being dominated based on belief. Intuitively, if
such a coalitional act profile
{
(
{
John
,
Mary
}
, Yung Kee
)
}
is consid-
ered by John and Mary (let's not bother why they would ever consider
such a coalitional act profile, which suggests that they should eat at
Yung Kee
- this is not in the scope of this example), then surely nei-
ther John nor Mary would object! They might be curious why the
other person does not object, but will be happy to accept the conse-
quence. Of course, they might later on change their private beliefs -
but again this is not in the scope of this example. Anyway, it is clear
that
{
(
{
John
,
Mary
}
, Yung Kee
)
}
is still a stable coalitional act pro-
file, and a member of the b-core, because the fact that both John and
Mary dine at
Yung Kee
is by all means a stable outcome.
{
(
{
John
,
Mary
}
, Yung Kee
)
}
Example 4.18
Consider again Example 4.4. As discussed in Ex-
ample 4.3, the core of the game is empty, because each coalitional
act profile is being genuinely dominated by at least one other coali-
tional act profile. However, the b-core of the game is not empty, and it
contains one coalitional act profiles, namely
{
(
{a, b, c},
movie)
}
.The
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