Explain the concept of value of perfect information in decision analysis. Give a real world example where the value of perfect information will be useful to a decision maker
The value of perfect information is the difference between the value with perfect information and the value without prior information at all. If the states of nature can be predicted beforehand, the decision-maker will only choose the alternatives which give the maximum payoff under any of the states of nature. In other words, unlike the no-information scenario, the deciision-maker will not to select just one alternative based on the expected payoff but can choose alternatives based on the states of nature predicted. Let us understand this with the following example.
Consider a firm has to make a decision about launching one of the three new products. The condition of the economy is unpredictable and has three states of nature, Excellent, Good, and Poor having prior estimates of the probability of occurrence 0.2, 0.5, and 0.3 respectively. The payoff scenario is as follows:
States of Nature | |||
Probability | 0.2 | 0.5 | 0.3 |
ALternatives | Excellent | Good | Poor |
Product 1 | 1000 | 400 | 200 |
Product 2 | 500 | 100 | 300 |
Product 3 | 300 | 500 | 0 |
Since no other information is available about the economy except for these prior probabilities, the expected payoff for launching Product 1 will be 1000 x 0.2 + 400 x 0.5 + 200 x 0.3 = 460, Similarly, for Product 2 and 3, the expected payoff will be 240 and 310 respectively. The decision-maker will choose Product 1 having the highest expected payoff of 460.
But suppose perfect information is available about the economy from some agent. The decision-maker will not compute the expected value for making a selection, He will wait for the agent's judgement and select accordingly. For example, if the agent's prediction is Excellent economy, the decision-maker will select Product 1 (for the highest payoff of 1000), for the prediction of Good/ Poor economy, he selects Product 2. So, the expected payoff, in this case, will be:
= 0.2 x (Best payoff of Excellent
economy) + 0.5 x (Best payoff of Good economy) + 0.2 x (Best payoff
of Poor economy)
= 0.2 x 1000 + 0.5 x 500 + 0.3 x 300
= 540
So, note that the expected payoff has increased from 460 (for no information case) to 540 (for perfect information case). So, the value of perfect information is 540 - 460 = 80
Explain the concept of value of perfect information in decision analysis. Give a real world example where the value of perfect information will be useful to a decision maker