The laplace method, Mathematics

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

Posted Date: 2/19/2013 2:48:04 AM | Location : United States







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