The b-Core: Belief-based Coalition Stability - Belief-based Stability in Coalition Formation with Uncertainty - page 104

Of course, this is not necessarily true in dynamic belief games where
agents are allowed to revise their beliefs throughout the game, but this
is out of the scope of this chapter. However, in general, the results
presented in topic still holds in ex-post analysis (see next session), and
in also ex-ante analysis where the beliefs of the agents are limited to
beliefs regarding other agents' preferences.
Example 4.21 Let us reconsider the scenario described in Example
4.2. For simplicity, we assume that the truth is that both Mary and
you prefer dining at Yung Kee together, to anything else. Otherwise,
eating together at any restaurant is better than eating alone, and all
restaurants other than Yung Kee is equally good (or bad). Finally, if
Mary or you have to eat alone, then there is no preference for restau-
rant - eating alone at any restaurant is equally miserable. However,
we also assume that both Mary and you have only the wrong beliefs.
That is, both of you unfortunately misbelieve that the other person
considers it the best option to eat alone, then eating together at any
restaurant is OK as long as it is not Yung Kee , and dining together
at Yung Kee is the least preferred option than anything else. If this is
the case, then by Theorem 4.3, any coalitional act would be OK. In-
tuitively, this can be understood as follows. For example, consider the
coalitional act that both of you eat at Spasso . According to the true
preferences, there is an objection to this coalitional act, that is, both
eating at Yung Kee . However, neither Mary nor you would raise this
objection, because both of you do not believe that this objection ex-
ists. We note also that according to the inaccurate beliefs, Mary would
have expected you to raise an objection of eating alone, and you would
also have expected the same objection to be raised by Mary. Surely, no
one would really raise this 'imagined objection' of eating along (which
might surprise Mary, and you, respectively), as this is not consistent
with the true preferences. Consequently, no objection, at all, will be
raised against the coalitional act that both of you eat at Spasso ,and
it becomes stable. The same reasoning process can be applied to all