Question

. Verizon LTE 5:02 PM 94% Problem 1 The following is a payoff table giving profits for various situations States of Nature Do Nothing What decision would a pessimist make? What decision would an optimist make! What decision would be made based on the realism criterion, where the coefficient of realism is 0.707 d. What decision would be made based on the equally likely criterion? e. What decision would be made based on the minimax regret criterion? Suppose now that the peobabilities of the 4 states of nature are known that is the probability to observe A is 35%, the probability to observe B is 30% the probability to observe C is 15%, and the probability to observe Dis 20%. Answer the following [ What decision would be made based on the expected monetary value? What is the EVPI?

Answer 1

	State 1	State 2	State 3	State 4
	0.35	0.3	0.15	0.2		EMV	Minimum	Maximum
Decision 1	1200	1400	1100	1800		1365	1100	1800
Decision 2	1100	1300	1600	1200		1255	1100	1600
Decision 3	1200	1700	1200	1100		1330	1100	1700
Decision 4	0	0	0	0		0	0	0
EVPI								Decision
column best	1200	1700	1600	1800		Minimax	500
						EMV	1365
						Maximin	1100
						Maximax	1800
						EV|PI	1530
						EVPI	165
Regret
	State 1	State 2	State 3	State 4		Expected	Maximum
	0.3	0.3	0.3	0.1
Decision 1	0	300	500	0		165	500
Decision 2	100	400	0	600		275	600
Decision 3	0	0	400	700		200	700
Decision 4	1200	1700	1600	1800		1530	1800

Formulas

Clipboard Font Alignment Number Styles Cells Editing Ideas Al i r fx | x A B Ε F G н State 1 0.35 1200 State 2 0.3 1400 1300 1700 3 Decision 1 4 Decision 2 Decision 3 6 Decision 4 State 3 0.15 1100 1600 1200 State 4 0.2 1800 1200 1100 1100 EMV =SUMPRODUCT($B$2:$E$2,B3:E3) =SUMPRODUCT($B$2:$E$2,B4:E4) =SUMPRODUCT($B$2:$E$2,B5:E5) =SUMPRODUCT($B$2:$E$2,B6:E6) Minimum =MIN(B3:E3) =MIN(B4:E4) =MIN(B5:E5) =MIN(B6:E6) Maximum =MAX(B3:E3) =MAX(B4:E4) =MAX(B5:E5) =MAX(B6:E6) 1200 Decision EVPI column best =MAX(B3:36) =MAX(C3:06) =MAX(D3:06) =MAX(E3:56) Minimax EMV =MIN(H22:H25) =MAX(G2:66) =MAX(H2:H6) =MAX(12:16) Maximin Maximax EVPL EVPI =SUMPRODUCT(B2:E2,B9:19) =H14-H10 Expected Maximum 19 Regret 20 21 22 Decision 1 23 Decision 2 24 Decision 3 25 Decision 4 26 27 State 1 0.3 =B$9-B3 =B$9-B4 =B$9-15 =B$9-B6 State 2 0.3 =C$9-C3 =C$9-04 =C$9-C5 =C$9-C6 State 3 0.3 =D$9-D3 =D$9-D4 =D$9-05 =D$9-D6 State 4 0.1 =E$9-E3 =E$9-E4 =E$9-E5 =E$9-E6 =SUMPRODUCT($B$2:$E$2,B22:E22) =MAX(B22:E22) =SUMPRODUCT($B$2:$E$2,B23:E23) =MAX(B23:E23) =SUMPRODUCT($B$2:$E$2,B24:E24) =MAX(B24:E24) =SUMPRODUCT($B$2:$E$2,B25:E25) =MAX(B25:E25)

a)
pessimist
Maximin = 1100 {any one of Alternative 1,2 and 3}

b)
optimist
maximax
= 1800
alternative 1

d)
equally likely

	State 1	State 2	State 3	State 4
	0.25	0.25	0.25	0.25		EMV
Decision 1	1200	1400	1100	1800		1375
Decision 2	1100	1300	1600	1200		1300
Decision 3	1200	1700	1200	1100		1300
Decision 4	0	0	0	0		0

1375 is maximum, hence alternative 1

e)
minimax = 500
Alternative 1

f)
max EMV   = 1365
alternative 1
g)
EVPI = 165