Consider a decision analysis problem whose potential profit payoffs are given by
ID: 412461 • Letter: C
Question
Consider a decision analysis problem whose potential profit payoffs are given
by the following table:
State of Nature
Alternative
S1
S2
S3
S4
A1
14
9
10
5
A2
11
10
8
7
A3
9
10
10
11
A4
8
10
11
13
If the decision maker knows nothing about the probabilities of the four states
of nature, which alternative should be chosen under: i) the maximax (optimistic) criterion, ii) the maximin (pessimistic) criterion and iii) the minimax regret criterion? Suppose that the payoff table in b) above represents costs rather than profits. Which alternative should be chosen using each of the same three criteria?
State of Nature
Alternative
S1
S2
S3
S4
A1
14
9
10
5
A2
11
10
8
7
A3
9
10
10
11
A4
8
10
11
13
Explanation / Answer
A.
Here by equating, we see A3 is more preferable than A2 as 11,10,10 vs 11,10,8 as decreasing precedence.
In case these are cost instead of profit.the orders are reveresed, Minmax becomes Maximin and vise versa
State of Nature Step 1 Max of each Alternative Max of Step 1 Maximax Alternative S1 S2 S3 S4 A1 14 9 10 5 14 14 A1 Ans 1 A2 11 10 8 7 11 A3 9 10 10 11 11 A4 8 10 11 13 13 State of Nature Step 1 Min of each Alternative Max of Step 1 Maximin Alternative S1 S2 S3 S4 A1 14 9 10 5 5 A2 11 10 8 7 7 A3 9 10 10 11 9 9 A3 Ans 2 A4 8 10 11 13 8 State of Nature Step 1 Max of each Alternative Min of Step 1 Minimax Alternative S1 S2 S3 S4 A1 14 9 10 5 14 A2 11 10 8 7 11 11 A2 Ans 3 A3 9 10 10 11 11 11 A3 Ans 3 A4 8 10 11 13 13Related Questions
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