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{
, which is reversed in Figure 4.5. This
edge is no longer an objection in the belief-based game because each
agent (wrongly) believes that the others would prefer a coalition of
size three to a coalition of size two. So although there is a real ob-
jection in this case, it will never be raised if everyone acts strictly
according to his beliefs. The same is true for the other two objections
whichleadfrom
(
{
a, b
}
,
movie)
,
(
{
c
}
,
movie)
}
{
(
{
a, b, c
}
,
movie)
}
to
{
(
{
a
}
,
movie)
,
(
{
b, c
}
,
movie)
}
and
. Effectively, these three original ob-
jections do not exist in the (incorrect) beliefs of the agents. Instead,
they are replaced by objections in the reverse direction. So in this
case, we can expect that the coalition structure
{
(
{
a, c
}
,
movie)
,
(
{
b
}
,
movie)
}
,
once somehow reached, would in fact be stable: although there are in
fact better coalition structures according to the concept of the core,
no agents realise this and they are happy to stay in the original node,
making it stable in practice.
{
(
{
a, b, c
}
,
movie)
}
Fig. 4.5
A belief-based dating game with wrong beliefs.
Example 4.5
Figure 4.6 shows the two-person game described in
Example 4.2 (for clarity, the coalition structures with only singleton
coalitions, e.g.,
,
are not shown in the figure as they are never preferred, and are always
objected to by other coalition structures without singleton coalitions).
The solid lines denote the real objections based on the players' real
{
(
{
John
}
,
Bonheur Restaurant
), (
{
Mary
}
,
Yung Kee
)
}
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