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