You are given the folloving payoff table in units of thousands of dollars) for a

Question

You are given the folloving payoff table in units of thousands of dollars) for a decision analysis problem. Consider the following payoff matrix. State of Nature Decision S1 220 200 0.6 S2. 170 180 0.3 110 150 0.1 Prior Probability a. Which alternative should be chosen under the maximin payoff criterion? b. Which alternative should be chosen under the maximax payoff criterion? c. Which alternative should be chosen under the expected value criterion? d. Which alternative should be chosen under the minimax regret payoff criterion? e. Do sensitivity analysis graphically with respect to the prior probabilities of states S and S2 (without changing the prior probability of state S3) to determine the crossover point where the decision shifts from one alternative to the other. Then use algebra to determine this crossover point. f. Repeat (e) for prior probabilities of states Si and S3. g. Repeat (e) for prior probabilities of states S2 and S3. h. If you feel that the true probabilities of the states of nature are within 10 percent of the given prior probabilities, which alternative would you choose?

Explanation / Answer

a)

For decision A1, min among S1,S2,S3 = 110

For decision A2, min among S1,S2,S3 = 150

Maximum among these is 150.

So maxmin payoff is 150.

Alternate A2 should be choosen

b)

For decision A1, max among S1,S2,S3 = 220

For decision A2, max among S1,S2,S3 = 200

Maximum among these is 220

So payoff for maximax is 220.

Alternate A1 should be choosen

c)

Expected value for A1 = 0.6*220+0.3*170+0.1*110 = 194

Expected value for A2 = 0.6*200+0.3*180+0.1*150 = 189

So expected payoff is 194.

Alternate A1 should be choosen

d) Regret table

So maximax regret payoff = max{40,20} = 40

Alternate A1 should be choosen

Decision S1 S2 S3 Maximin A1 220-220 = 0 180-170 = 10 150-110 = 40 40 A2 220-200 = 20 180-180=0 150-150=0 20

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