Example Application of the b-Core: Buyer Coalition Problem with Beliefs - Belief-based Stability in Coalition Formation with Uncertainty - page 119

Problem with Beliefs

for the purpose of computing a solution. These are not realistic as-
sumptions.
Thus, instead of assuming each agent to know one another's prefer-
ences, it is more reasonable to model such information as each agent's
beliefs regarding the others' preferences, as done in many traditional
A.I. and epistemological approaches. The difference here is that beliefs,
unlike knowledge, are fallible instead of being objectively accurate, and
may differ from agent to agent.

5.1.4 Existing Approaches

The first two concerns are partly handled by Asselin and Chaib-Draa
[12], who propose a non-transferable payoff model, in which the buyer
agents send their preferences to a central agent, and Pareto optimal so-
lutions are found using an exact set cover algorithm. This work targets
Pareto optimal solutions and not the stricter and more stable criterion
of the core. Later, Chan and Leung [13] propose a distributed mech-
anism and corresponding strategies that aim at reaching core-stable
solutions.
In this chapter, we build upon the foundation of these previous
work by also taking the third concern (privacy of information) into
account.

5.1.5 A New Approach

Instead of assuming the buyer agents to have reservation prices for
items, we only require them to have explicit preference orders regarding
possible types of coalition (and this is a relaxed requirement which
makes the mechanism much more applicable in real life).
Thus, instead of using social utility, we use the game theoretic
concepts of the core, and Pareto e ciency, as well as the b-core, as