Mavzu: O’yinlar nazariyasi masalasini chiziqli programmalashtirish masalasiga keltirish


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8-mavzu. O‘yinlar nazariyasining predmeti va asosiy tushunchalar 444

Yechish. Chiziqli programmalashtirishning ikkilanish masalalari juftini tuzamiz.
To‘g‘ri masala:




shartlarni qanoatlantiruvchi



funksiyaning maksimum qiymatini toping.

Iikkilanish masalasi:




shartlarni qanoatlantiruvchi



funksiyaning minimum qiymatini toping.


To‘g‘ri va ikkilanish masalasining optimal rejasini topamiz(1-jadval).
1-jadval

i

Bazis

CB

P0

1

1

1

1

0

0

P1

P2

P3

P4

P5

P6

1
2
3
4

1
2
3


4

1
2
3


4

P4
P5
P6
P4
P3
P6
P2
P3
P6



0
0
0
0
1
0
1
1
0

1
1
1
0

1
1
1


1

1/2
1


1/2
3/2

1
1
2
-1

1
1
2


0

1/2
1


3/2
1/2

2
0
1
-1

2
0
1


-1

1
0
0


0

0
1
0
-1

0
1
0


0

0
1
0


0

1
0
0
0

1
0
0


0

1/2
0


-1/2
1/2

0
1
0
0

0
1
0


1

0
1
0


1

0
0
1
0

0
0
1


0

0
0
1


0

1-jadvaldan ko‘rinib turibdiki, to‘g‘ri masala optimal rejaga, ikkilanish masalasi esa optimal rejaga ega. Demak, o‘yin bahosi



optimal strategiyalar esa



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