The following payoff table shows profit for a decision analysis problem with two
ID: 3290968 • Letter: T
Question
The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature: The probabilities for the states of nature are P(s_1) = O.65, P(s_2) = 0.15, and P(s_3) = 0.20. (a) What is the optimal decision strategy if perfect information were available? (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? What is its expected value? If required, round your answer to one decimal place. (d) What is the expected value of perfect information?Explanation / Answer
Solution:
a) Optimal decision strategy
S1 : d1
S2 : d1 or d2
S3 : d2
b) Expected value of decision strategy developed in part (a):
= 0.45*(S1d1) + 0.25*(S2d1) + 0.3*(S3d2) (S2d1 = S2d2)
= 0.45*250 + 0.25*100 + 0.3*150 = 182.5
c) Without perfect info:
Lets compute for both d1 & d2
d1: 0.45*250 + 0.25*100 + 0.3*100 = 167.5
d2: 0.45*200 + 0.25*100 + 0.3*150 = 160
Hence d1
Expected value as calculated above: 167.5
d) EVPI = EV|PI - EMV = 182.5 - 167.5 = 15
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