Conclusion - Belief-based Stability in Coalition Formation with Uncertainty - page 170

agents' preferences to be publicly known, and that each agent has
perfect knowledge about the outcomes of their cooperation. This as-
sumption is often not practical.
Thus, game theory is not perfect for modelling human. But, how
about game theory for modelling software agents?
The answer in this case seems to be 'yes'. Unlike their human count-
parts, software agents in semi-competitive applications are typically
modelled as rational and self-interested entities. Thus, for a computer
scientist creating such agent-based systems, game theory can be a very
useful tool. In fact, game theoretical solution concepts have already
been used to evaluate the qualities of multi-agent coalition formation
mechanisms.
There is still one limitation, however. Like human being, software
agents are also far from being omniscient. That is, they act according
to some private beliefs (whatever their system input provides them)
and they have to rely on whatever evidences they can perceive, or
their past experience, during their decision making. And like their
human counterparts, their past experiences are error-prone. Although
game theory has its potential in multi-agent applications, it has to be
extended.
Several possible extensions have already been proposed. One pos-
sible solution for handling this limitation could be the stochastic ap-
proaches [3] recently proposed in transferable utility cooperative games.
However, while these works provide new solutions concepts for TU
games with uncertainty, they cannot be applied in NTU games. The
reason is that utilities are not always transferable in real-life multi-
agent applications, or, that there may be simply not enough samples
to produce a meaningful probabilistic distribution in some cases.
For these reasons, we are proposing three types of new cooperative
games that are based on agents' private beliefs instead of common
knowledge in this topic.
First, in order to handle internal uncertainties regarding the en-
vironmental states, we proposed the NTU-IU games, and the corre-