Conclusion - Belief-based Stability in Coalition Formation with Uncertainty - page 171

sponding solution concepts of the strong core and the weak core. The
idea is that, instead of classifying each coalitions as simply 'stable' (i.e,
in the core) or not, as done in the traditional approaches, we divide
the obtainable consequences of a coalition into three stability classes:
those that are certainly stable (strong core), those that maybe stable
(weak core) depending on the agents' conflict resolution strategy, and
those that are certainly not stable. We also see how the strong core,
the weak core and the core are affected by the precision of the agents'
beliefs regarding the environment: the more refined the beliefs are, the
smaller the weak-cores are and the larger the strong cores are.
Second, in order to handle agents' beliefs regarding one another's
preferences, we propos the NTU-PB games, and the corresponding so-
lution concepts of the b-core. The key idea is that any objection that
is not consistent with the beliefs of all coalition members will never be
raised, and therefore any coalitions with only such non-raisable objec-
tions should be treated as stable coalitions. We also discuss the effect
of beliefs accuracy on the stability of NTU-PB games. In particular,
we see that a decrease in accuracy of in agents' beliefs actually leads
to more stable results. We also discuss how the b-core can be used to
evaluate a multi-agent coalition formation problem, namely, the buyer
coalition problem.
Finally, we discuss how to combine the proposed concepts into a
single type of games, the NTU-BU games, and the four corresponding
solution concepts of sb-core, wb-core, s-core and w-core. By doing so,
we are able to provide useful stability concepts for these private belief-
based NTU games which otherwise cannot be analysed properly using
the traditional approaches. We believe that our model provides a useful
tool in evaluating coalition formation algorithms for multi-agent-based
cooperative games.