1 answer

Statement attached Q3) The following matrix gives the payoffs in utiles (a measure of utility) for...

Question:

statement attached

Q3) The following matrix gives the payoffs in utiles (a measure of utility) for three alternatives and three possible states

Q3) The following matrix gives the payoffs in utiles (a measure of utility) for three alternatives and three possible states of nature: State of Nature S2 A2 A3 Which alternative would be chosen under (1) the Laplace principle (2) the Maxi-Max rule (3) the Hurwicz rule with a=0.75

Answers

The answer to Q 3:

1. The Laplace Principle:

Step 1: Calculate P for each row.

n= 3 (Three alternatives)

P= 1/3(P1+P2+P3)

State of Nature

S1

S2

S3

Expected Payoff

A1

50

80

80

1/3(50+80+80)

A2

60

70

20

1/3(60+70+20)

A3

90

30

60

1/3(90+30+60)

Step 2: Select the maximum Pay off from the expected payoff

State of Nature

S1

S2

S3

Expected Payoff

A1

50

80

80

70

A2

60

70

20

50

A3

90

30

60

60

Chosen Alternative A1.

2. The Maxi-max Rule:

Step 1: Find the maximum of each row.

State of Nature

S1

S2

S3

Maximum Payoff

A1

50

80

80

80

A2

60

70

20

70

A3

90

30

60

90

Step 2: Select the maximum from the column of maximum pay off.

State of Nature

S1

S2

S3

Maximum

A1

50

80

80

80

A2

60

70

20

70

A3

90

30

60

90

Chosen alternative: A3 S1.

3. The Hurwicz Rule:

Step 1: Identify the maximum and minimum of each row:

State of Nature

S1

S2

S3

Maximum

Minimum

A1

50

80

80

80

50

A2

60

70

20

70

20

A3

90

30

60

90

30

Step 2: Calculate P for each alternative.

State of Nature

S1

S2

S3

Maximum

Minimum

H

A1

50

80

80

80

50

72.5

A2

60

70

20

70

20

57.5

A3

90

30

60

90

30

75

p= α*maximum+(1-α)*Minimum

For A1, P=0.75*80+(1-0.75)*50

For A2, P = 0.75*70+(1-0.75)*20

For A3, P = 0.75*90+(1-0.75)*30

Step 3: Select the maximum payoff from column H

The highest payoff is with alternative A3.

.

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