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only cause some stable coalitions formed under misunderstanding to
emerge.
Finally, we consider the cases where some, but not all, of the agents'
beliefs regarding an otherwise valid objection are inaccurate, that is,
the objection is incorrectly not believed to exist by some of the agents.
Then in this case any dynamic updates in beliefs still will not affect the
b-core. The reason is that according to the definition of the b-core, in
order for an objection to be considered as raisable, it is only required
that at least one of the agents in the deviating coalition to believe that
the objection exists. So any dynamic updates in beliefs will only cause
some of the previously non-believing agents to change their beliefs
accordingly after the objection has been raised by a believing agent,
but that will have no effects on the b-core, according to the definition,
since the end results would be the same no matter it is objected to by
one agent or multiple agents.
Similarly, an agent that updates his beliefs dynamically after his
proposal is turned down would have no effect on the b-core, because
that objection was an invalid one according to our definitions, both
before and after the update. The only effect might be that the agent
will not make the proposal again (as he is rational). While this may
have effects on the path or even outcome of negotiation, the set of
stable coalitional act profiles is not affected, since the solutions that
were reachable and stable remain the same set.
4.7 Summary
Most classical solution concepts in non-transferable utility coalitional
game theory rely on a public information assumption. That is, they
assume the agents' preferences to be publicly known. However this
assumption is not practical in many software agent applications where
intelligent agents have to rely on their private beliefs during decision
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