The following is a payoff table giving profits for various situations. What is the expected value of perfect information?
A)7.6
B)8.4
C)8.8
D)9.2

Question

The following is a payoff table giving profits for various situations.  What is the expected value of perfect information?
A)7.6 
B)8.4 
C)8.8 
D)9.2

Quizplus · Accepted Answer

To find the expected value of perfect information, we first need to calculate the expected value (EV) for each decision:
EV for Decision 1 = (0.3 x 10) + (0.4 x 5) + (0.3 x 0) = 4.5
EV for Decision 2 = (0.4 x 8) + (0.5 x 4) + (0.1 x 0) = 5.2
Next, we need to calculate the EV of each state of nature:
EV of State A = (0.5 x 10) + (0.3 x 8) + (0.2 x 6) = 8.2
EV of State B = (0.4 x 5) + (0.5 x 4) + (0.1 x 3) = 3.9
EV of State C = (0.3 x 0) + (0.4 x 2) + (0.3 x 4) = 1.8
Finally, we can calculate the EV with perfect information (EVPI) by taking the maximum EV of the states of nature and subtracting from it the EV of the decision without perfect information:
EVPI = max(EV of State A, EV of State B, EV of State C) - max(EV for Decision 1, EV for Decision 2)
EVPI = 8.2 - 5.2 = 3
Thus, the best choice is to choose Decision 2 with an EV of 5.2. If perfect information were available, the optimal decision would be to choose Decision 1 with an EV of 4.5 only if the state of nature is B or C, but to choose Decision 2 with an EV of 8.2 if the state of nature is A. However, the EV of perfect information is only 3, which is less than the difference in expected values between Decision 2 and Decision 1 without perfect information (5.2 - 4.5 = 0.7). Therefore, it is not worth the cost of obtaining perfect information.

The Following Is a Payoff Table Giving Profits for Various