Please perform computerized solution, not handwritten. Thanks The table represen
ID: 3263610 • Letter: P
Question
Please perform computerized solution, not handwritten. Thanks
The table represents payoffs contingent upon certain acts and events occurring. Identify any inadmissible acts. Determine the optimum act using: b. the maximum expected payoff criterion. c. the maximin payoff criterion. d. the maximum likelihood technique e. the maximax criterion. f. the Laplace method. g. Compute EVPI. Convert the payoffs to regrets (opportunity losses) and determine the optimum act using: h. the minimum weighted regret. i. the minimax criterion. j. the maximum likelihood technique.Explanation / Answer
a. An act is inadmissible if it is dominated by some other act, where domination is defined as below.
An act 'A' dominates an act 'B' if the payoff of 'A' is as high as that of 'B' in all the events and higher in at least one of the events.
Hence, A-5 is inadmissible as it is dominated by A-2. (Inadmissible acts are not considered in the calculation of optimum acts)
b. Maximum expected payoff criterion
We calculate the expected payoffs for each act (multiply payoff by row's probability and sum the products) and choose the one with the highest value of expected payoff. The following table shows the results.
Now, since, A-3 has the highest expected payoff (=109) hence it is the optimum act.
c. Maximin payoff criteria
It is based on finding the MAXimum of MINimums. For every act, we find the minimum payoff over each event (that is, take the minimum of each column). Then, take the maximum of the 'column minimums'. The act having the maximum value is optimum.
As A-3 has the maximum value of 'column minimum' (=70), therefore A-3 is the optimum act.
d. Maximum likelihood technique
We take the most likely event (tha is, the event having the highest probability) and ignore all others. Then, consider the act having the highest payoff under the most likely event; that event is considered as optimum.
Since probability of E-2 is maximum (=0.5), we consider only event 2. Under event 2, the payoff of A-1 (=90) is the highest among all the acts. Hence, A-1 is the optimum act.
e. Maximax payoff criteria
It is based on finding the MAXimum of MAXimums. For every act, we find the maximum payoff over each event (that is, take the maximum of each column). Then, take the maximum of the 'column maximums'. The act having the maximum value is optimum.
As A-3 has the maximum value of 'column maximum' (=200), therefore A-3 is the optimum act.
f. Laplace method
In this method, we assume each event to occur with equal probability, i.e P(E1)=P(E2)=P(E3)=1/3. Under this assumption, we calculate the expected payoff of each act and choose the one with maximum value.
Since A3 has the highest payoff (=113.33) hence it is the optimal act.
g. EVPI: Expected Value of Perfect Information
EVPI = Expected payoff under certainty Maximum Expected Payoff
EVPI = 123 (from the table) - 109 (from part (b)) = 14
For parts h, i and j, we convert payoffs to opportunity losses by subtracting the payoffs from the largest payoff possible under that event (that is, subtract each entry from the row's maximum). The opportunity losses are given in the following table
Now, the optimal act is determined in the same way as we did in case of payoffs. The only difference is that now we aim to minimize the opportunity loss, hence we take all the minimum values as the best options.
Prob A1 A2 A3 A4 A6 Payoff Payoff X Prob Payoff Payoff X Prob Payoff Payoff X Prob Payoff Payoff X Prob Payoff Payoff X Prob E1 0.3 4 1.2 100 30 200 60 20 6 70 21 E2 0.5 90 45 80 40 70 35 60 30 10 5 E3 0.2 10 2 60 12 70 14 90 18 90 18 Expected Payoff 48.2 82 109 54 44