Three decision makers have assessed utilities for the following decision problem (payoff in dollars).Decision Alternative10080The indifference probabilities are as follows.50Payoff Decision Maker A20d₁d₂-20-1001.000.950.900.700.500.00$1 $2Decision Maker B should choose ??20 50 -20Decision Maker C should choose ??$380 100 -100Decision Maker B1.000.600.500.350.150.00Decision Maker C1.000.900.750.600.40If P(S₁) = 0.25, P(S₂) = 0.50, and P(S3)= 0.25 and all decision makers assign a utility of 10 to the greatest payoff and a utility of 0 to the smallest payoff, find a recommended decision for each of the three decision makers. (Note: For the same decisionproblem, different utilities can lead to different decisions.)Decision Maker A should choose ?? ✓0.00

Given data: Payoff Table: Decision Alternative S1 S2 S3 d1 20 50 -20 d2 80 100 -100 P(S1)=0.25P(S2)=0.50P(S3) =0.25 Solution: Decision maker Table A Decision Alternative S1 S2 S3 d1 0.70 0.90 0.50 d2 0.95 1.00 0.00 The expected utility for the decision maker A (Decision 1): EU(d1) =∑Si×PSi=0.70× 0.25 + 0.90×0.50+0.50×0.25 = 0.750 (Decision 2): EU(d2) =∑Si×PSi =0.95×0.25+1×0.50+0×0.25 =0.7375 Here EU(d1) > EU(d2), then decision maker of A, EU(d1) is suggested. Decision maker Table B State of nature Decision Alternative S1 S2 S3 d1 0.35 0.50 0.15 d2 0.60 1.00 0.00 The expected utility for the decision maker B: EU(d1) =∑Si×PSi=0.35×0.25+ 0.50×0.50+0.15×0.25 =0.375 EU(d2) =∑Si×PSi=0.60×0.25+ 1.00×0.50+0.00×0.25 =0.65 Here EU(d2) > EU(d1), then the decision maker of B, EU(d2) is suggested. Decision maker Table-C State of nature Decision Alternative S1 S2 S3 d1 0.60 0.75 0.40 d2 0.90 1.00 0.00 The expected utility for the decision maker C: EU(d1) =∑Si×PSi = (0.60)×0.25+ (0.75)×0.50+(0.40)×0.25 =0.625 EU(d2) =∑Si×PSi=(0.90)×0.25+ (0.1)×0.50+(0.00)×0.25 =0.275 Here EU(d1) > EU(d2), then decision maker of C, EU(d1) is suggested. Hence, Decision Maker A should choose =(d1)Decision Maker B should choose =(d2)Decision Maker C should choose =(d1)