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Problem with Beliefs
non-transferable utility approach where the focus is on achiev-
ing stable solutions (e.g, in term of the core, the b-core and
Pareto e
ciency). We will also study a new distributed mech-
anism that is designed to encourage the participating agents
to propose incremental improvements toward stable solution.
At the end of the chapter, we will demonstrate by experi-
ment that the proposed mechanism is able to reach core-stable
solutions in over 99% of the cases according to the b-core, and
it is a big improvement over the existing approaches.
5.1 Buyer Coalition Problems
In this chapter, we see how the stability concept of the b-core can be
used to analyse mechanisms for solving a real-life problem, the buyer
coalition problem.
Many sellers in real-life offer some kind of volume discounts to cus-
tomers buying large quantity of their products. Typically there are
more than one product on sale, together with non-increasing price
schedules such that the more units of the same type are bought to-
gether, the bigger the offered discount is.
In order to take advantage of such price schedules, a new business
model known as group buying (sometimes called collective buying,
team buying, or 'store mobbing') has emerged in recent years. In e-
commerce, some applications, known as on-line buyer coalitions [1-3],
have emerged in both B2C (e.g., [4-6]) and B2B platforms (e.g., [7]).
These applications allow on-line buyers to team up so that they can
collectively place a larger order to enjoy the volume discount.
In many cases, the various products are substitutable, meaning that
each buyer needs exactly one unit of any of the products, although he
may have different preferences regarding the various items of the same
type. For example, a buyer may only want to buy exactly one camera
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