The b-Core: Belief-based Coalition Stability - Belief-based Stability in Coalition Formation with Uncertainty - page 76

have very good Blanquette de veau there. What do you think?

• Mary: Well, if you insist, let's try that.

You: This is good. I like French food, too.
• Mary: See you at 7 p.m. at Bonheur .
• You: Yap. See you then.
The coalition resulted from this conversation is a stable one, with
the outcome that both you and Mary eat at Bonheur Restaurant .This
is because at the end of the conversation, both Mary and you believe
that there is no better alternative. Of course, as we have discussed,
a better alternative is actually Yung Kee , as Mary and you both like
Kung Pao chicken there.

•

To model this situation of coalition stability under uncertainty of
other players' preferences, we are proposing another stability criterion,
the belief-based core, or b-core , that also takes into accounts the beliefs
of the agents. We believe the proposed concepts can provide useful
solution concepts for this type of coalitional games, which we call non-
transferable utility games with private beliefs.

4.2 Belief-based Coalitional Games

In this section we illustrate the ideas of belief-based coalitional games
by studying two examples of games that are stable in practice, despite
they are not stable in the traditional core. The existence of these ex-
amples suggests that such belief-based games are not well handled by
the core-based approach.
For the sake of ease of understanding of the subsequent discussion,
we can imagine that the coalition formation process will follow the
standard propose-and-evaluate format, that is, at each round of the
mechanism, one agent is allowed to make proposal (in private) to his
intended targets, who can then either accept or reject. If no agreement
can be reached, the default coalition structure would be that each