Multi-agent Cooperation and Stability - Belief-based Stability in Coalition Formation with Uncertainty - page 10

a group of all three.
However, because they do not know the real preference of each
other, they wrongly believed that the other person will not be inter-
ested in such a proposal. John is aware of the situation. However, as a
self-interested and rational agent, he decides to propose to Peter and
Mary the most preferred choice of John, which is also the local can-
teen in a group of all three. Peter and Mary, not realizing that there
is actually a better viable option, accepted John's proposal, resulting
in a three-agent coalitions for the canteen.
We can argue that this coalition, although seemingly sub-optimal,
is actually stable. John has proposed the best coalition according to
his own private beliefs and preferences, and both Peter and Mary have
selected the most appropriate actions based on their beliefs and pref-
erence.
Secondly, regarding the agents being non-omniscient, suppose also
that all three agents have heard a rumour that a third restaurant is
offering a discount for the day. If the rumour is true then all three of
them prefer to go there, but not otherwise. Obviously, in this case, the
stability of the above coalition would depend on not only the agents'
beliefs, but also on how the agents' decisions are affected by such
uncertainty caused by the rumour. The coalition proposed by John
would neither be certainly stable nor certainly unstable.
It is obvious that, such situations, although being straight forward
enough, cannot be captured by the current game models. So there is
actually a discrepancy in assumptions when we apply these traditional
games stability concepts to multi-agent coalition formation problems,
especially in NTU games where little works has been done on this
subject.
Instead, what we need for multi-agent applications is a stability
model that is based on private beliefs instead of common knowledge,
and that agent omniscience is not assumed. We will develop such mod-
els in this topic. Our contribution in this work is as follows. We shall
extend the classic stability concept of the non-transferable utility core