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be extended. We introduce a new stability concept, namely the
b-core
. We will study a belief-based stability criterion which
we labelled the belief-based core, and give examples to illus-
trate how the new concept can be used to provide both
ex-ante
and
ex-post
analysis of coalition formation mechanisms.
4.1 Games Without Common Knowledge
Two research directions in coalition formation can be identified. First,
we have the works in mechanism design, where many coalition forma-
tion mechanisms have been proposed. In order to analyse the stability
and e
ciency of the outcome of such mechanisms, or to provide
ex-
ante
prediction for the possible outcomes, we need the models from
the other research direction, namely, the various stability concepts in
coalitional game theory. So far, most of these stability concepts have a
common knowledge assumption, meaning that various characteristics
of a game, including each individual agent's preference, are known to
all agents, before a game theoretic analysis is possible. However, this
assumption is not realistic in belief-based agent systems, where the
agents' decisions are based on agents' private beliefs instead of com-
mon knowledge. In this chapter, we continue our discussion on the
second research direction and discuss a belief-based stability concept.
In traditional non-transferable utility games, the specification of all
agents' preferences regarding each possible consequence obtainable by
the coalition are supposed to be publicly known for certain, meaning
that each agent knows not just its own preferences, but also (correctly)
the preferences of all others as well. However, in a typical multi-agent
setting, such an assumption is only valid when all agents voluntarily
disclose all their preferences and private beliefs to one another during
coalition formation, but this is, obviously, not something that will
occur in most applications. Indeed, in many cases, the agents would not
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