Two Classes of Stability — Strong Core and Weak Core - Belief-based Stability in Coalition Formation with Uncertainty - page 33

means that the agent believes that there are no better options. From
this point of view, a coalition is stable if only if every member of the
coalition 'prefers' it, and no one has the intention to quit his coalition,
given his experience and beliefs. This is even the case if these beliefs
are uncertain, which might be caused by, for example, conflicts in the
agents' past experience.
In conclusion, we need a game theoretic model for modelling uncer-
tainty in beliefs and uncertainty caused by unobservable environmental
information.
In the literature, there have been several extensions of the concept
of 'the core,' proposed for modelling coalitional games with uncer-
tainty. For instance, a stochastic payoff approach has been proposed in
[3] and a Bayesian core in [4]. These new proposals handle the problem
of uncertain beliefs in transferable utility games and stochastic coop-
erative games. However, while these works provide good theoretical
foundation on their respective application areas, they are not suit-
able to handle problems such as the buyer coalition formation game
described above. This because these models usually assume that the
probability distributions of different parameters are known. However,
in the buyer coalition formation games that we have just described,
the samples (i.e., the agent's purchase experience) are often too sparse
to provide any meaningful estimation of the probability distributions,
which these approaches rely on. Instead, what we need here is a generic
stability model for non-transferable cooperative games.
In this chapter we will illustrate a rule-based approach in under-
standing stability under uncertainty. We will develop a model where
each agent processes some private beliefs that can be used for decision
making. However, private beliefs are not always without uncertainty
(for example, two similar items in the buying history may have dif-
ferent quality), which means that they may conflict with one another.
Thus the stability of a coalition game depends not only on the observ-
able attributes and the decision rules of each agent, but also on how
such conflicts are resolved by each agent.