Two Classes of Stability — Strong Core and Weak Core - Belief-based Stability in Coalition Formation with Uncertainty - page 28

Chapter 3
Two Classes of Stability — Strong
Core and Weak Core
The quest for certainty blocks the
search for meaning. Uncertainty is the
very condition to impel man to unfold
his powers.
Erich Pinchas Fromm
E ciency and stability are two important concepts in coalition
formation analysis. One common assumption in many well
known criteria such as the core and Pareto e ciency is that
there exists a publicly known value for the grand coalition
and each and every sub-coalition. However, in software agent
applications, this assumption is often not true as the agents
generally do not know the exact coalition values, at least not
for certain. Instead, agents have to rely on whatever evidences
they might observe, and evaluate those evidences according to
their private information based on past experience in order to
have an estimation of the value of the sub-coalitions, or even
that of the grand coalition.
As we mention in the previous Chapter, there are two main
sources of uncertainty here. First, the private information that
each agent has (or estimates) is often uncertain belief in na-
ture, and may even be self-conflicting. Second, the agents,
which are heterogeneous and autonomous, may have different
conflicting resolution strategies.
Consider the situation when you propose to dine out with