Two Classes of Stability — Strong Core and Weak Core - Belief-based Stability in Coalition Formation with Uncertainty - page 29

your new girlfriend Mary. According to your observation, Mary
seems to quite like Chinese food, so you decide to find a good
Chinese restaurant to enjoy a good meal with her. Unfor-
tunately, you are not so familiar with the Chinese restau-
rants, and basically have no idea which restaurant is really
the best. From you limited experience, Yung Kee is proba-
bly the best among those you have tried. However, most of
your friends suggest that the best should not be Yung Kee ,
as Royal Szechuan is actually much better, though you have
been there once and the experience there was terrible. Worse,
if you do not bring Mary to the best Chinese restaurant, then
you probably will be in trouble as you really should not show
your ignorance before your new girlfriend who is an expert in
Chinese food. Technically, your preference (choosing Yung Kee
or Royal Szechuan ) is dependent on something that you are
not sure of, which in turn affects the stability of the coalition
consisting of you and Mary. Such uncertainties make the tradi-
tional approaches unfit for many real-world problems, except
perhaps, in idealised scenarios.
In this chapter, we extend traditional solution concepts,
including the core and Pareto optimality, by proposing a new
rule-based stability concepts under uncertain environment:
the CU-Core .
3.1 Coalition Formation and Stability
Many coalition formation mechanisms have been proposed in the past.
An outcome of such mechanisms is a set of coalitions. As a coalition
that will fall apart is not very useful, a natural requirement for the
produced coalitions is that they must be stable. In order to analyse
the stability and e ciency of such coalitional games, many models