The following payoff table shows profit for a decision analyses problem with two

Question

The following payoff table shows profit for a decision analyses problem with two decision alternatives and three states of nature: The probabilities for the states of nature are P(s_1) = 0.45, P(s_2) = 0.25, and P(s_3) = 0.3. (a) What is the optimal decision strategy if perfect information were available? S_1: d1 S_2: d1 or d2 s_3: d2 (b) what is the expected value for the decision strategy developed in part (a)? If required, round your answer to one decimal place. (c) Using the expected value approach, what is the recommended decision without perfect information? d2 What is its expected value' If required, round your answer to one decimal place. (d) What is the expected value of perfect information' If required, round your answer to one decimal place.

Explanation / Answer

Solution:

Expected value with perfect information (EVwPI) = 300*0.45 + 150*0.25 + 100*0.3 = 202.5

Expected value of d1 = 300*0.45 + 150*0.25 + 75*0.3 = 195

Expected value of d2 = 250*0.45 + 150*0.25 + 100*0.3 = 180

Therefore recommended decision is d1

Expected value EVmax = 195

Expected value of perfect information (EVPI) = EVwPI - EVmax = 202.5 - 195 = 7.5

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