The Laplace method
Laplace method employs all the information by assigning equal probabilities to the possible payoffs for every action and then selecting such alternative which corresponds to the maximum expected pay off
Illustration
A company is considering investing in one of three investment opportunities A, B and C under specific economic conditions. The payoff matrix for this condition is economic situation
|
Investment opportunities
|
1 £
|
2 £
|
3 £
|
|
A
|
5000
|
7000
|
3000
|
|
B
|
-2000
|
10000
|
6000
|
|
C
|
4000
|
4000
|
4000
|
Find out the best investment opportunity by using the given criteria:
i. Maximax
ii. Maximin
iii. Minimax
iv. Hurwicz as Alpha = 0.3
Solution
Economic condition
|
Investment opportunities
|
1 £
|
2 £
|
3 £
|
Minimum £
|
Maximum £
|
|
A
|
5000
|
7000
|
3000
|
3000
|
7000
|
|
B
|
-2000
|
10000
|
6000
|
-2000
|
10000
|
|
C
|
4000
|
4000
|
4000
|
4000
|
4000
|
i. By using the Maximin rule Highest minimum = £ 4000
Select investment C
ii. By using the Maximax rule Highest maximum = £ 10000
Select investment B
iii. Minimax Regret rule
|
|
1
|
2
|
3
|
Maximum regret
|
|
A
|
0
|
3000
|
3000
|
3000
|
|
B
|
7000
|
0
|
0
|
7000
|
|
C
|
1000
|
6000
|
2000
|
6000
|
Select the minimum of the maximum regret that is £3000
Select investment A
iv. Hurwicz rule: expected values
For A (7000 x 0.3) + (3000 x 0.7) = 2100 + 2100 = £4200
For B (10000 x 0.3) + (-2000 x 0.7) = 3000 + 1400 = £ 1600
For C (4000 x 0.3) + (4000 x 0.7) = 1200 + 2800 = £ 4000
Best outcome is £ 4200 select investment A