The following profit payoff table shows profit for a decision analysis problem w

Question

The following profit payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:

The probabilities for the states of nature are P(s1) = 0.5, P(s2) = 0.3 and P(s3) = 0.2.

What is the optimal decision strategy if perfect information were available?

What is the expected value for the decision strategy developed in part (a)? If required, round your answer to one decimal place.

Using the expected value approach, what is the recommended decision without perfect information?



What is its expected value? If required, round your answer to one decimal place.

What is the expected value of perfect information? If required, round your answer to one decimal place.

Explanation / Answer

There are two decision alternatives and three states of nature and the payoff matrix.

Under perfect information

If we are certain about nature of state to be S1 then d1 is prefered as it will result in higher profits of 300 as compared to 200 for d2.

In case of certainty of S2 both are equally likely as profits of 175 remains the same.

In case of S3 profits are higher in case of d2 so it is preferred over d1.

The expected monetary value (EMV) for the decision alternatives are calculated by using the formula for expected value as follows:

EMV for d1 = 300*(0.5) + 175*(0.3) + 50*(0.2) = 150+51.5+10 = 211.5

EMV for d2 = 200*(0.5) + 175*(0.3) + 100*(0.2) = 100+51.5+20 = 171.5

Therefore in the absence of perfect information and using the criteria of maximization of expected profits d1 is preferred over d2 because of higher EMV

In order to find the value of perfect information, the formula used is :

Value of perfect information = Expected gain under perfect information - Expected maximum gain in absence of PI = [ 300*(0.5) + 175*(0.3) + 100*(0.2) ] - 211.5 = 221.5 - 211.5 = 10

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.