Question

	State	of	Nature
Decision Alternative	s1	s2	s3	s4
d1	600	400	-100	120
d2	700	-200	0	400
d3	700	-200	0	400
P(si)	0.3	0.4	0.2	0.1

For a lottery having a payoff 700 with probability p and -200 with probability (1-p), the decision maker expressed the following indifference probability. Suppose U (700) =100 and U (-200) =-10.

Payoff	Indifferent Probability
600	0.95
400	0.8
120	0.5
0	0.35
-100	0.2

a) Complete the utility table by using the above payoff and indifference probabilities.

	s1	s2	s3	s4
d1
d2
P(si)	0.3	0.4	0.2	0.1

b) Find the optimal decision for the decision maker by using expected utility approach.

Answer 1

Given

a)

	State	of	Nature
Decision Alternative	s1	s2	s3	s4
d1	600	400	-100	120
d2	700	-200	0	400
d3	700	-200	0	400
P(si)	0.3	0.4	0.2	0.1

maximum value = 700

minimum value = -200

utility value(700) =100

utility value(-200) =10

pay off	indifferent probability
600	0.95
400	0.8
120	0.5
0	0.35
-100	0.2

And for utility value we get p(sj)*(100-(-10))-10

pay off	indeference probability	Utility
700	not applicable	100
700	not applicable	100
600	0.95	94.5
400	0.8	78
120	0.5	45
0	0.35	28.5
-100	0.2	12
-200	not applicable	-10

	s1	s2	s3	s4
d1	94.5	78	12	45
d2	100	-10	28.5	78
P(si)	0.3	0.4	0.2	0.1

b) A strategy is strongly domestic, when compare to other strategies.

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