Problem 2 You are given the following payoff table (in units of thousands of dol
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Problem 2 You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem. Consider the following payoff matrix. State of Nature Decision 110 150 0.1 A1 220 200 0.6 170 180 0.3 Prior Probability a. Which alternative should be chosen under the maximin payoff criterion? b. Which alternative should be chosen under the maximax payoff criterion? c. Which alternative should be chosen under the expected value criterion? d. Which alternative should be chosen under the minimax regret payoff criterion? e. Do sensitivity analysis graphically with respect to the prior probabilities of states Si and S: (without changing the prior probability of state S) to determine the crossover point where the decision shifts from one alternative to the other. Then use algebra to determine this crossover point. f Repeat (e) for prior probabilities of states Si and S g. Repeat (e) for prior probabilities of states S2 and S h. If you feel that the true probabilities of the states of nature are within 10 percent of the given prior probabilities, which altemative would you choose? tates)Explanation / Answer
Preparatory Work
Pay-off Table with related calculations
Decision
State of Nature
Row max
Row min
EMV
S1
S2
S3
A1
220
170
110
220
110
194
A2
200
180
150
200
150
189
Probability
0.6
0.3
0.1
EMV = sum(pay-off x probability)
Part (a)
For maximin criterion, we evaluate for each decision, the minimum pay-off over the SON and opt for that decision which has the maximum of these minimum pay-off.
Clearly, 150 > 110 and hence optimum decision is: A2 ANSWER
Part (b)
For maximax criterion, we evaluate for each decision, the mxiimum pay-off over the SON and opt for that decision which has the maximum of these maximum pay-off.
Clearly, 220 > 200 and hence optimum decision is: A1 ANSWER
Part (c)
Under expected value criterion, we evaluate for each decision, EMV, which is nothing but the sum(pay-off x probability) and chose that decision which has the maximum EMV.
Clearly, 194 > 189 and hence optimum decision is: A1 ANSWER
Part (d)
First we develop the Regret Pay-off Table, wherein we find the best pay-off under each SON over the decisions and once this is located, the regret for the other decisions is obtained as the difference between the best pay-off and the pay-off for the decision.
Regret Pay-off Table
Decision
State of Nature
Row max
S1
S2
S3
A1
0
10
40
40
A2
20
0
0
20
Since 20 is minimum of the two maximum regret pay-offs,
optimum decision is: A2 ANSWER
Decision
State of Nature
Row max
Row min
EMV
S1
S2
S3
A1
220
170
110
220
110
194
A2
200
180
150
200
150
189
Probability
0.6
0.3
0.1
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