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Step-by-Step Exercises on Decision Making under Risk - EMV and EVPI BSNS2120, J. Wang Name __Jinchang Wang___ A payoff table is given as below. States of Nature A B C Alternatives P(A)=0.7 P(B)=0.1 P(C)=0.2 1 120 -100 60 2 90 100 70 3 80 100 80 4 -50 80 90 Show your calculations in Part 1 and Part 2. Part 1. What is the best decision? – Do the two steps below. Step 1. Calculate EMV (expected payoff) of each alternative: EMV(Alt. 1) = 120*0.7 + (-100)*0.1 + 60*0.2 = 84 +(-10) + 12 = 86 EMV(Alt. 2) = 90*0.7 + 100*0.1 +70*0.2 = 63 + 10 +14 = 87* EMV(Alt. 3) = 80*0.7 + 100*0.1 + 80*0.2 = 56 +10 +16 = 82 EMV(Alt. 4) = (-50)*0.7 + 80*0.1 + 90*0.2 = -35 +8 +18 = -9 Step 2. Pick up the alternative with highest EMV, which is _alternative 2_ . Your answer to Part 1 question: The best decision is selecting Alternative _2_ whose expected payoff is _87_. Part 2. What is EVPI (expected value of perfect information) ? – Do the three steps below. Note: EVPI = (EV with PI) (EV without PI) Step 1. EV without PI = Expected payoff of your decision without using additional PI In Part 1, you made decision without using additional PI: Your decision: Alternative _2_ , EMV of the decision: _87______ . Therefore, EV without PI = Max EMV = 87. Step 2. Calculate (EV with PI). If PI says ‘A will occur’, then you would select Alternative __1__ with payoff _120_ . If PI says ‘B will occur’, then you would select Alternative _2 or 3_ with payoff _100_ . If PI says ‘C will occur’, then you would select Alternative __4__ with payoff _90_ . The probability for PI to say ‘A will occur’ is _0.7__ . The probability for PI to say ‘B will occur’ is _0.1___ . The probability for PI to say ‘C will occur’ is _0.2___ . The expected payoff with PI = sum of all possible payoffs weighted by their probabilities = 120*0.7 + 100*0.1 +90*0.2 = 84 + 10 + 18 = 112 Step 3. EVPI = (EV with PI) (EV without PI) = _112 – 87 _ = _25__ This is your answer to Part 2 question. Part 3. Part 1 and Part 2 can be put in the extended Payoff table. (1) Put your results in Part 1 and Part 2 into the extended payoff table below. Alternatives 1 2 ○ 3 4 column Max States of Nature A B C P(A)=0.7 P(B)=0.1 P(C)=0.2 120 -100 60 90 100 70 80 -50 120 100 80 100 80 90 90 EMV’s (expected values) 120*0.7+(-100)*0.1+60*0.2 = 86 90*0.7+100*0.1+70*0.2 = ○ 87 80*0.7+100*0.1+80*0.2 = 82 (-50)*0.7+80*0.1+90*0.2 = -9 120*0.7+100*0.1+90*0.2 = 112 (2) Circle and label your decision and its EMV you calculated in Part 1 in the table. (3) Circle and label (EV without PI) and (EV with PI) in the table. EVPI = EVvPI – EVw/oPI = 112 – 87 = 25.