The Complete Picture: sb-core and wb-core - Belief-based Stability in Coalition Formation with Uncertainty - page 146

agent may have regarding the other agents' preferences: after
all, during a decision making process, an agent will not only
consider his preferences, but also the assumed preferences of
his fellow participants also. These two types of uncertainties
have impacts on coalition's stability in software agent systems
just as they do in real life.
In this chapter, we shall revisit the classic stability concept
of the core, and we shall propose new belief-based stability
criteria based on these two types of uncertainty considerations.
We shall see how the new concept can be applied in stability
analysis of belief-based coalition formation game.
6.1 Uncertain Opinion and Private Beliefs
In this chapter, we first provide a summary of the concepts we have
developed so far in this topic. We will review the stability criteria
developed in the previous chapters, After that, the various components
will be put together and the main results of this topic, namely, the wb-
core and the sb-core will be presented.
Most existing stability concepts in games theory have a common
knowledge assumption. Indeed, it is often assumed that the various
characteristics of the game, including the preferences of each individ-
ual participant, are well known to all participants. Even more, everyone
is assumed to know the private secrets of each other without any un-
certainty. Needless to say, such a model is not very practical in the real
world, apart from answering theoretical what-if questions for scenarios
with such a common knowledge assumption.
To the computer scientists, this assumption certainly does not help
much either. As software agent systems in the virtual world are com-
monly based on private beliefs instead of common knowledge. This can
be seen in the famous B.D.I architecture [1], as well as some application