Two Classes of Stability — Strong Core and Weak Core - Belief-based Stability in Coalition Formation with Uncertainty - page 32

private beliefs. For example, the buyer agents may need to surf on-
line catalogues to look for suitable products on sale. Thus, in this
case, the observable environmental information includes the various
attributes of the items being sold, for examples, the product names,
brand names, the item's locations, and the seller names. However, some
of items' attributes (e.g., the quality of the items) are not observable,
or not verifiable, at the time of purchase. Such information that is not
observable introduces uncertainties into the coalitional game. Worse,
the agents' preferences do depend on such inaccessible information.
For example, an agent would join a buyer coalition in order to be able
to buy items at a lower price. However, he might not have been willing
to join should he know in advance that the quality of the items was
terrible. On the contrary, one might not be willing to join a coalition
to buy things from a particular seller because the volume discount the
seller offers is not attractive. However, he would have changed his mind
if he knew that the items were of the best quality!
One thing that the agents can do in this uncertain situation is
to match those observable attribute values against similar cases from
their previous purchase experience, and then estimate the value of
the hidden attributes. For example, the buyer may want to consider
the quality of previously bought items of the same brand and from
the same seller. This way, each agent can have an estimation of the
quality of the various items on sale, which in turn influences the agent's
decision of whether to join any buyer coalition.
Therefore, for the buyer coalition formation problem, an agent can
obtain private beliefs of the hidden environmental information (e.g.,
the quality of the current items on sales), given the observable item
attributes (e.g., the brand name and name of the seller), and then he
can use these estimations as a basis to evaluate each of the possible
coalitions. Thus, for each agent, the problem now becomes a series of
classification problems: the task of each agent is to classify each pos-
sible coalition as either 'preferred' or 'not preferred,' where 'preferred'