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, an optimal
strategy for player II is the uniformly concentrated distribution in
B
0
,where
B
0
can
be for example
An optimal strategy for player I is the uniform distribution o
n
F
=
{
(
,
)
,
(
,
)
,
(
,
)
,
(
,
)
,
(
,
)
,
(
,
)
,
(
,
)
,
(
,
)
,
(
,
)
,
(
,
)
,
(
,
)
,
B
0
1
1
1
2
1
3
1
4
2
1
2
2
2
3
2
4
3
1
3
2
3
3
(
,
)
,
(
,
)
,
(
,
)
,
(
,
)
,
(
,
)
,
(
,
)(
,
)
,
(
,
)
,
(
,
)
}
4
1
4
2
5
1
5
2
6
1
6
2
7
1
7
2
8
1
and the value of the game
745
100
.
v
=
Example 7.
A factory distributes its product to eight different areas. The factory
sends 1,000 units of the product to each one of the eight distribution centers, C
1
,C
2
,
...,C
8
, once a week. In these centers the product is submitted to a quality control by
the respective inspection services. The inspection service of each one of the centers
C
i
chooses one unit of the product out of the 1,000 in the series to inspect. If the unit
selected does not meet the requirements, then the service inspects all the series, and
the company has to pay a fine of c
i
times the number of faulty units in this series.
The management of the factory knows that they produce
s
faulty units every
week and wants to distribute these among the different areas, thus minimizing the
fine. The number of faulty products,
s
=
85. The fine that must be paid to center
C
i
for every faulty product found is
c
1
=
10
,
c
2
=
10
,
c
3
=
15
,
c
4
=
15
,
c
5
=
15
,
c
6
=
15
,
c
7
=
20
,
c
8
=
30
.
With these parameters we obtain the values
r
i
,
a
i
,
b
i
and
α
i
summarized in the following table:
r
i
a
i
b
i
α
i
15.45 15
0.45 16
15.45 15
0.45 16
10.30 10
0.30 10
10.30 10
0.30 10
10.30 10
0.30 10
10.30 10
0.30 10
7.72
8
−
0.27
8
5.15
5
0.15
5
To tal 85.00 83
d
=
2 85
An optimal strategy for player I is the same that in the previous ca
se
, an optimal
strategy for player II is the uniformly concentrated distribution in
B
0
,where
B
0
can be
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