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Traditional game theory concepts such as NTU games and the core
are insu
cient in modelling games with uncertain beliefs, such as the
game in Section 3.2. The reason is that we are actually facing a new
type of games where the outcome is uncertain, yet is not probabilistic.
We propose a model for this type of games as illustrated in Figure
3.1, which we call Non-transferable Utility Games with Internal Un-
certainty (NTU-IU games). We formally define this new type of games
in Definition 3.1.
Fig. 3.1
Non-transferable utility game with uncertainty.
Definition 3.1 (NTU-IU Game)
An NTU-IU game is a tuple
g
=
N,E,
(
I
i
)
,H,X,
(
P
i
)
,
defined as follows.
•
N
=
{
1
,...,n
}
is a set of agents, with any subset
C
⊆
N
of it
called a coalition.
•
E
=
{
(
a
1
=
v
1
)
∧
(
a
2
=
v
2
)
∧···∧
(
a
k
=
v
k
)
}
is the evidences that
are observable by each of the agents, where each
a
i
is the name of
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