the laplace methodlaplace method employs all the

Question

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