Question

The following profit payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature: State of Nature Decision Alternative Si S2 S3 d1 300 175 50 d2 200 175 100 The probabilities for the states of nature are P(51) = 0.5, P(52) = 0.3 and P(53) = 0.2. a. What is the optimal decision strategy if perfect information were available? Si : di S2: di or d2 S3 : d2 b. What is the expected value for the decision strategy developed in part (a)? If required, round your answer to one decimal place. 222.5 c. Using the expected value approach, what is the recommended decision without perfect information? di 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. 10.0

Answer 1

a.

If perfect information is available, the highest payoff for each state of nature would be selected.

Therefore, the optimal decision strategy shall be as follows:

S1: d1 (300)

S2: d1 or d2 (175)

S3: d2 (100)

b.

Expected value with perfect information = Sum of ( Maximum payoff in State of nature x Probability of State of nature)

= ( 300 x 0.5) + ( 175 x 0.3) + ( 100 x 0.2)

= 150 + 52.5 + 20

= 222.5

c.

Expected value without perfect information = Maximum Expected monetary value (EMV)

EMV = Sum of ( Payoff in State of nature x Probability of State of nature)

Therefore,

EMV of d1 = ( 300 x 0.5) + ( 175 x 0.3) + ( 50 x 0.2) = 150 + 52.5 + 10 = 212.5

EMV of d2 = ( 200 x 0.5) + ( 175 x 0.3) + ( 100 x 0.2) = 100 + 52.5 + 20 = 172.5

Since d1 has the maximum EMV, the recommended decision would be to select d1.

Expected value of d1 = 212.5

d.

The expected value of Perfect information = Expected value with Perfect information - Maximum EMV

= 222.5 - 212.5

= 10