Question

Using the provided payoff table and prior probability, determine the alternative that maximizes the likelihood strategy. Which alternative should be selected based on this analysis?

Alternative High Medium Low A 20 20 5 B 25 30 11 C 30 12 13 D 10 12 12 E 50 40 -28 Prior Probability 0.3 0.2 0.5

a) Alternative A
b) Alternative B
c) Alternative C
d) Alternative E

Answer 1

To determine the alternative that maximizes the likelihood strategy, we need to calculate the expected value for each alternative and select the one with the highest expected value.

Step-by-step explanation:

To determine the alternative that maximizes the likelihood strategy, we need to calculate the expected value for each alternative and select the one with the highest expected value. The expected value is calculated by multiplying each payoff by its corresponding prior probability and summing up these values.

Calculating the expected values for each alternative:

Expected value of Alternative A = (20 x 0.3) + (20 x 0.2) + (5 x 0.5) = 6 + 4 + 2.5 = 12.5

Expected value of Alternative B = (25 x 0.3) + (30 x 0.2) + (11 x 0.5) = 7.5 + 6 + 5.5 = 19

Expected value of Alternative C = (30 x 0.3) + (12 x 0.2) + (13 x 0.5) = 9 + 2.4 + 6.5 = 17.9

Expected value of Alternative E = (50 x 0.3) + (40 x 0.2) + (-28 x 0.5) = 15 + 8 + (-14) = 9

Based on this analysis, Alternative B should be selected as it has the highest expected value of 19.