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Fig. 3.2
Effect of refineness on strong-core and weak-core.
the value of the hidden prevailing state. This is equivalent to a con-
ventional common knowledge game where the opinion of each agent
consists of the prevailing state only, i.e.,
B
i
=
{s
∗
}
for all
i ∈ N
.Itis
easy to see that the core, and strong core and the weak core are the
same in such a common knowledge game.
However, in general this is not true in most real-life non-common-
knowledge games. To understand this, we formally define the concept
of
correct opinions
.
Definition 3.11 (Correct Opinion and Correct Opinion Game)
Given an NTU-IU game
g
=
N,E,
(
I
i
)
,H,X,
(
P
i
)
with agent's opinions
O
=(
B
1
,B
2
,...,B
m
)
,
we say an agent's opinion
B
i
is
correct
if
s
∗
∈
B
i
.Furthermore,wesay
the game
g
is a
correct opinion game
if the opinion
B
i
of agent
i
∈
N
is correct for all
i
∈
N
.
It should be noted that we do not require agent
i
to have
s
∗
only in
his opinion
B
i
for his opinion to be correct. We only require that
s
∗
is
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