Information Technology Reference
In-Depth Information
Fig. 3.5
Sets
B
0
for
n
=
4,
m
=
10 and the two values of
s
, 11 and 18
Example 2.
Let us consider the OEIG with
n
10. An optimal strategy
for player I is the uniform distribution on the set of his pure strategies,
=
4and
m
=
F
.If
s
=
18,
H
}
then (
3.30
) is satisfied, therefore the value of the game is equal to
v
=
min
{
H
,
K
m
n
,
K
and
K
defined by (
3.23
)and(
3.24
) respectively. In
K
m
n
and
H
=
where
H
=
this case
K
=
K
=
3
,
000
,
1
,
800
,
therefore
K
<
K
,
H
<
H
. Then the value of the game is
1
,
800
10
4
H
=
v
=
=
0
.
18
an
d an optimal strategy for player II is the uniformly concentrated distribution on
B
0
,where
B
0
is
B
0
=
{
(
i
,
j
)
:1
≤
j
≤
9
,
for
i
=
1
,
2
}.
A representation of this set can be seen in Fig.
3.5
.If
s
=
11, then (
3.30
)isalso
satisfied. In this case
K
=
=
,
,
,
,
K
1
274
5
000
K
,
H
H
. Then the value of the game is
therefore
K
<
<
1
274
10
4
,
v
=
H
=
=
0
.
1274
Search WWH ::
Custom Search