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little mutual misunderstanding among the agents (or that the misun-
derstandings have no effect on the outcomes).
4.6 On Dynamic Beliefs
Before we end the chapter, we discuss the applicability of the presented
results in games where the agents are allowed to revise their beliefs
dynamically. As we mentioned earlier in this Chapter, our discussions
so far have assumed a static belief model. So for the ex-post analyses,
since all beliefs are treated as static in nature in these analyses, the
results presented in this topic will hold. However, ex-ante analyses, on
the other hand, do allow dynamic belief models. However, even in this
case, our results will hold for the games where the agents' beliefs are
limited to their belief regarding other agents' preferences, which is the
assumption in our model. We briefly elaborate this in the following.
First, if all agents' beliefs regarding an otherwise valid objection
are all inaccurate, that is, the objection is not believed to be in exis-
tence by any agent, then this objection will never be raised, and any
dynamic updates in beliefs will not occur because such objections sim-
ply will not be known. From an observer's point of view, such a case is
unfortunate because the truth will never be known to the community.
This might not, however, be a bad thing to happen, because in general
we will have more number of stable coalitions formed under mutual
misunderstanding, as we have shown that the core is always a subset
of the b-core.
Second, if all agents' beliefs regarding an otherwise valid objection
are all accurate, then in this case dynamic updates in beliefs is not
needed because everyone's beliefs (that the objection does not exist)
are correct in the first place, so there is nothing to update. In other
words, the situation is effectively the same as the 'ideal' case in which
all agents are omniscient. Any modification to the agents' beliefs will
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