Consider a decision analysis problem whose potential profit

Consider a decision analysis problem whose potential profit payoffs are given

by the following table:

State of Nature

Alternative

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

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	13

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

Consider a decision analysis problem whose potential profit

Solution

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