Player A would prefer to have the largest value possible from those highlighted. In the diagram this can be seen to occur when the line V = 2 + 7X intersects with V= 6 - 3X which occurs at the point as determined below.

Value of the game is as follows.

The minimax criteria is to maximise the minimum values. To find the solution for B's strategy we need to identify and solve the 2 by 2 pay-off matrix associated with A's optimal strategy. In this case that will be the columns associated with the lines V= 2 + 7X and V= 6 - 3X. Hence

3

9

6

2

Q3.

a) Solution:

The transformation is as follows.

Total Number of audience = 10000000

Total audience size as a pair in each matrix element = 100000

Total value of a pair in each matrix element = 10000000/100000 = 100

Subtracting half the total value of a pair as computed above from each element of the payoff matrix defined in the question.

Half the total value = 50

Payoff Matrix

SkyCast

Historical

Drama

Comedy

Contemporary

Drama

Variety

Mini Series

60 - 50

58 - 50

49 - 50

52 - 50

RayTV

Detective

55 - 50

52 - 50

54 - 50

59 - 50

Film

55 - 50

54 - 50

47 - 50

55 - 50

Variety

47 - 50

54 - 50

56 - 50

61 - 50

Transformed Matrix:

SkyCast

Historical

Drama

Comedy

Contemporary

Drama

Variety

Mini Series

10

8

-1

2

RayTV

Detective

5

2

4

9

Film

5

4

-3

5

Variety

-3

4

6

11

b) Solution:

SkyCast

Historical

Drama

Comedy

Contemporary

Drama

Variety

Mini Series

10

8

-1

2

RayTV

Detective

5

2

4

9

Film

5

4

-3

5

Variety

-3

4

6

11

Comparing fourth column with the third column 2 > -1, 9 > 4, 5 > -3...

In the diagram this can be seen to occur when the line V = 2 + 7X intersects with V= 6 - 3X which occurs at the point as determined below.

The minimax criteria is to maximise the minimum values. To find the solution for B's strategy we need to identify and solve the 2 by 2 pay-off matrix associated with A's optimal strategy. In this case that will be the columns associated with the lines V= 2 + 7X and V= 6 - 3X. Hence

The value decides the type of the show to be put out in order to maximise the ratings over the coming TV season. The value against Detective has more gain (approximately 3.33) and hence it has to be put out in order to maximise the ratings.
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