Example Application of the b-Core: Buyer Coalition Problem with Beliefs - Belief-based Stability in Coalition Formation with Uncertainty - page 116

from a seller even if there are multiple models on sale, although he
may have different preferences for the various models. The challenge
here is to find a good partition of the buyers into non-overlapping
buying coalitions, with each coalition placing an aggregate order for
one product from a single seller. Such a partition is called a buyer
coalition structure (coalition structure).
Several multi-agent system-based approaches have been proposed
for this problem, with the majority focusing on reaching optimal or
near optimal coalition structures in terms of social utility maximiza-
tion. That is, the focus of most approaches is on the amounts of saved
money compared with some reference selling price. The more money is
saved, the higher the utility for that player is. The total amount saved
from all buyers is used as the social utility.
One of such early work is [8], which is a centralized incremental
mechanism where the next most profitable coalition is greedily formed
in each step of the mechanism. Later, a genetic algorithm-based ap-
proach is proposed in [9] and a multi attribute approach is proposed
in [10] where each buyer's decision is based on an analytic hierarchy
process [11].
In these approaches, each buyer agent is assumed to have his reser-
vation prices for the products, which represents the highest amounts
that the agent is willing to pay for the items. A buyer's utility is de-
fined as a monotonic increasing function of the difference between the
reservation price and the actual price it ends up paying for the item
it acquires. The goal of such mechanisms is thus to find a coalition
structure that maximizes the sum of the individual member agent's
utility (i.e., the social utility). These social utility-based approaches
thus imply a transferable utility model. The stability of the coalitions
are not considered.