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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
 
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