Example Application of the b-Core: Buyer Coalition Problem with Beliefs - Belief-based Stability in Coalition Formation with Uncertainty - page 120

measurements of the coalitions' quality.
We shall follow a mechanism plus strategy approach: we first in-
troduce a distributed non-transferable utility mechanism and discuss
two strategies, one of them is belief-based and the other one not. We
first show that both of these two strategies, if followed by the agents,
can produce core-stable and b-core stable solutions in over 97% of the
time according to a series of test cases, which make our mechanism a
stable one even with the consideration of private beliefs.
We then compare the two strategies from the agents' point of view,
and show that they achieve similar results in term of agents' prefer-
ences, but the belief-based strategy is much more e cient in term of
message costs. It is to the benefits of the agent to adopt that strategy.

5.2 Background of Buyer Coalition Problem

5.2.1 Unit Price Schedule and Agent Preference

In this chapter, we follow the problem setting of [12] and [13].
Suppose that there are m type of substitutable products

G = { g 1 ,g 2 ,...,g m }

being sold, and n buyers agents

N = { a 1 ,a 2 ,...,a n } ,

each interested in buying one unit of any of the products. A non-
increasing unit-price schedule is associated with each product so that
the unit price decreases with the number of units bought together in
the same order.
In order to take advantage of the price schedule, the buyers form
coalitions, such that for each product g i , there is one (possibly empty)