Question

statement attached

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

Answer 1

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.