Question

investment	poor	average	good
A	50	75	20
B	80	15	40
C	-100	300	50

Maximax, Maximin, Minimax Regreat, Hurxicz 0.4, Equal liklihood

Answer 1

a.

Maximum payoff of investment A=75

Maximum payoff of investment B=80

Maximum payoff of investment C=300

Maximax=Maximum of (Maximum payoff of the investment alternatives A,B,C)

=Maximum of(75,80,300)

=300

Hence,the decision is to choose investment C

b.

Minimum payoff of investment A=20

Minimum payoff of investment B=15

Minimum payoff of investment C=-100

Maximin=Maximum of (Minimum payoff of the investment alternatives A,B,C)

=Maximum of(20,15,-100)

=20

Hence,the decision is to choose investment A

c.

Maximum payoff of investment A=75

Maximum payoff of investment B=80

Maximum payoff of investment C=300

Minimax=Minimum of (Maximum payoff of the investment alternatives A,B,C)

=Minimum of(75,80,300)

=75

Hence,the decision is to choose investment A

d.

Hurwicz ,alpha=0.4

In this case,

Payoff for an investment =alpha *Maximum payoff+(1-alpha)*Minimum payoff

payoff of investment A=0.4*75+0.6*20=42

payoff of investment B=0.4*80+0.6*15=41

payoff of investment C=0.4*300+0.6*(-100)=60

Hence,the decision is to choose investment C

e.In equal likelihood,prob(good)=prob(average)=prob(poor)=1/3=0.3333

payoff of investment A=0.3333*(50+75+20)=48.33

payoff of investment B=0.3333*(80+15+40)=45

payoff of investment C=0.3333*(-100+300+50)=83.33

Hence,the decision is to choose investment C