Conclusion - Belief-based Stability in Coalition Formation with Uncertainty - page 172

7.2 The Future
We would like to end this topic by pointing out several possible future
research directions in belief-based games non-transferable utility game
theory.
Firstly, so far this topic has focused on extending the core-based so-
lution concepts. The core is one of the most popular solution concepts,
but there are also other solution concepts that worth study, such as
the stable sets [4] and the nucleoli [5]. It is interesting to see how the
criteria proposed in this topic can be extended into these concepts.
However, the solutions are not trivial. The definition of stable sets
itself, for instance, involves a recursive definition. This implies that
the agents must have some common knowledge regarding the current
stable sets, which seems to contradict the private information assump-
tion.
Secondly, dynamic updates of beliefs can be considered. Intelli-
gent agents have the ability to learn from past interactions with other
agents, and update their beliefs dynamically during a game. This direc-
tion will lead to dynamic versions of the proposed solution concepts.
To handle this, we need to define rules for agents' beliefs updating
during the coalition formation process. Instead of the commonly used
propose-and-evaluatate cycles, we now have a three-step cycle, namely
belief update, proposal and evaluatation. We also need to define the
concept of reachable solutions. The idea is that, starting from some
initial configuration, a reachable solution is one where there exist some
paths, following some valid update/proposal/evaluation cycles, to that
solution. The criterion of the b-core can then be extended by allowing
only reachable solutions.
Finally, other types of beliefs of the agents can be considered as
well. So far we have considered (first level) beliefs of an agent regarding
the other agents' preferences, but how about more complex ones such
as second or higher level beliefs? However, the problems are more com-