The Complete Picture: sb-core and wb-core - Belief-based Stability in Coalition Formation with Uncertainty - page 147

examples (e.g., [2], [3])
Such beliefs result in two types of uncertainty. First, as discussed
in Chapter 3, an agent's preference (or desire) depends on the agent's
opinions regarding the environment, but in the real world, such opin-
ions are sometimes uncertain, which means that an agent is often un-
certain about his preference as well.
As an example, suppose that the preference of a company is to form
a joint venture partnership with a strategic partner if they believe that
the economy will rebounce in the following year. However, because of
the global financial crisis, they are receiving conflicting forecasts from
various financial consultants. As a result they are uncertain about the
upcoming economy. Thus, in this case, they are not too certain about
their own preference regarding the partnership either. As we stated in
Chapter 3, the strong core and the weak core can be used to handle
such uncertainties.
Second, as discussed in Chapter 5, we see that an agent's action
also depends on his private belief of the other agent's preference. Con-
tinuing with the above example, suppose that both the company and
its potential partner believe that the global financial crisis is going to
end, the global economy will rebounce, and hence they should form a
coalition to grasp the opportunity. However, even in such a case, one
more requirement must be met before the coalition materializes, that
is, as least one of the two companies needs to correctly believe that the
other company is interested in such a deal (or at least it should not
rule out such a possibility). Otherwise, even if this is the preferred and
logical option for both companies, if both of them failed to recognize
that there is a potential partnership, then none of them is likely to
propose the idea to the other party at the first place because making
such a proposal would be inconsistent with their belief regarding the
other company. In Chapter 4, the b-core is introduced to model such
a private belief-based game.
Thus, we see that such uncertain opinions and private beliefs have
effects on the stability of a coalition formation game, and they are