Question

4. Which Alternative a decision-maker will choose if he/she uses the maximax criterion on the problem below? Which Alternative a decision-maker will choose if he/she uses the maximin criterion on the problem below? Which Alternative a decision-maker will choose if he/she uses the equally likely criterion on the problem below? Please show the process of your answer.

	States of Nature
	1	2	3
Alternative A	50	55	60
Alternative B	30	50	80
Alternative C	70	80	70
Alternative D	-100	-10	140

Answer 1

Solution:

(a) Maximax criterion: In maximax criterion, maximum of each alternative is determined first. Then, the maximum of the maximum values is chosen as an alternative.

From the given information, maximum value for each alternative is determined below,

Alternative A = Max (50, 55, 60) = 60

Alternative B = Max (30, 50, 80) = 80

Alternative C = Max (70, 80, 70) = 80

Alternative D = Max (-100, -10, 140) = 140

Using Maximax criterion,

Max (60, 80, 80, 140) = 140

Answer: Alternative D

(b) Maximin criterion: In maximin criterion, minimum of each alternative is determined first. Then, the maximum of the minimum values is chosen as an alternative.

From the given information, minimum value for each alternative is determined below,

Alternative A = Min (50, 55, 60) = 50

Alternative B = Min (30, 50, 80) = 30

Alternative C = Min (70, 80, 70) = 70

Alternative D = Min (-100, -10, 140) = -100

Using Maximin criterion,

Max (50, 30, 70, -100) = 70

Answer: Alternative C

(c) Equally likely criterion: In equally likely criterion, average payoff for each alternative is determined first. Then, the alternative with the highest average payoff is selected.

From the given information, average payoff for each alternative is determined below,

Alternative A = (50 + 55 + 60) / 3 = 55

Alternative B = (30 + 50 + 80) / 3 = 53.33

Alternative C = (70 + 80 + 70) / 3 = 73.33

Alternative D = (-100 -10 + 140) / 3 = 10

Using equally likely criterion,

Max (55, 53.33, 73.33, 10) = 73.33

Answer: Alternative C