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more preferred than
x
2
.
Example 3.10
For comparison, suppose instead that the opinion
of agent
A
3
were
B
3
=
{
Average
,
Bad
}
.Inthiscase,rulesP2toP4
would have been fired, but not P1.
Example 3.11
The situation would have also been different should
the preference rules of
A
3
have included a new rule
{
Good
,
Average
}⇒
x
2
3
x
1
such that the complete set
P
3
of preference rules of
A
3
is as follows:
P1.
{
Good
}⇒
x
2
3
x
1
P2.
x
1
3
x
2
P3.
{
Bad
}⇒x
1
3
x
2
P4.
{
Average
}⇒
{
Average
,
Bad
}⇒
x
1
3
x
2
P5.
x
2
3
x
1
In this case, with an opinion
B
3
=
{
Good
,
Average
}⇒
,rulesP1,
P2 and P5 in
P
3
will be fired, and consequently agent
A
3
will have
conflicting preferences.
{
Good
,
Average
}
More precisely, we have the following definitions.
Definition 3.2 (Agent Opinion)
The
opinion function
O
i
(
·
,
·
)of
agent
i
N
is a mapping from evidences and the agent's experience,
to the agent's opinion. Given an NTU-IU game
∈
g
=
N,E,
(
I
i
)
,H,X,
(
P
i
)
,
we define
an opinion B
i
of agent
i
∈
N
to be a set
B
i
=
{
b
i
1
,...,b
ik
}
=
O
i
(
E,I
i
)
⊆
V
H
,
such that for each
b
ij
∈
B
i
there is an experience rule
e
ij
in
I
i
,where
e
ij
is the rule
E
→
b
ij
.
Having defined the agent opinions, we can give a definition for
agent preferences given the opinions as follows.
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