The matrix below gives payoffs in thousands of dollars for

The matrix below gives payoffs in thousands of dollars ($) for four alternatives and three possible

Solution

a)

Average of A1 = 1/4 * (30 + 20 + 30 + 60) = 35

Average of A2 = 1/4 * (80 + 50 + 70 + 10) = 52.5

Average of A3 = 1/4 * (70 + 90 + 40 + 20) = 55

Average of A4 = 1/4 * (10 + 60 + 30 + 50) = 37.5

Thus, by laplace principle, one should choose altenative A3 which has the highest average value

b)

Under Minimax rule , the option with least regret is choosen

option      MaxRegret

A1            60

A2            80

A3           90

A4            60

hence option A3 is choosen under Minimax rule

c)

Under Maximax rule, the option with best payoff is choosen

option      best payoff

A1             60

A2             80

A3              90

A4              60

hence option A3 is choosen under Maximax rule

d)

weighted payoff of A1= 0.8 * 60 + 0.2 * 20 = 52

weighted payoff of A2 = 0.8 * 80 + 0.2 * 10 = 66

weighted payoff of A3 = 0.8 * 90 + 0.2 * 20 = 76

weighted payoff of A4 = 0.8 *60 + 0.2 * 10 = 50

hence under Hurwicz rule with a=0.8 , option A3 is choosen