Question

Three decision makers have assessed utilities for the following decision problem (payoff in dollars):

	State of Nature
Decision Alternative	S1	S2	S3
d1	30	40	-20
d2	80	100	-80

The indifference probabilities are as follows:

	Indifference Probability (p)
Payoff	Decision maker A	Decision maker B	Decision maker C
100	1.00	1.00	1.00
80	0.95	0.80	0.85
40	0.85	0.70	0.75
30	0.75	0.55	0.60
-20	0.60	0.25	0.50
-80	0.00	0.00	0.00

Find a recommended decision for each of the three decision makers, if P(s₁) = 0.15, P(s₂) = 0.70, and P(s₃) = 0.15. (Note: For the same decision problem, different utilities can lead to different decisions.) If required, round your answers to two decimal places.

Decision maker A

EU(d1) =

EU(d2) =

Recommended decision:

Decision maker B

EU(d1) =

EU(d2) =

Recommended decision:

Decision maker C

EU(d1) =

EU(d2) =

Recommended decision:

Answer 1

Decision maker A

Utility table

	s1	s2	s3
d1	0.75	0.85	0.6
d2	0.95	1	0

EU(d1) = 0.15*0.75+0.70*0.85+0.15*0.6 = 0.7975

EU(d2) =  0.15*0.95+0.70*1+0.15*0 = 0.8425

Recommended decision : d2

Decision maker B

Utility table

	s1	s2	s3
d1	0.55	0.7	0.25
d2	0.8	1	0

EU(d2) =  0.15*0.55+0.70*0.7+0.15*0.25 = 0.61

EU(d1) = 0.15*0.8+0.70*1+0.15*0= 0.82

Recommended decision : d2

Decision maker C

Utility table

	s1	s2	s3
d1	0.6	0.75	0.5
d2	0.85	1	0

EU(d2) =  0.15*0.6+0.70*0.75+0.15*0.5= 0.69

EU(d1) = 0.15*0.85+0.70*1+0.15*0 = 0.8275

Recommended decision : d2