Perfect Information

I do know that perfect information was tested in the June exam – it is the only time it has ever been tested in F5 because it was not in the syllabus before. It is actually very unlikely to be tested in this Decembers exam. Also, it is not directly related to drawing decision trees – it applies to any example of decision making under uncertainty whether or not we draw a tree to help us.

However, I will explain with a very simple example.

Suppose we have to choose between to choices A and B, and suppose the return from each depends on the level of demand – high demand or low demand.

The returns from A will be 20 if low, and 100 if high
The returns from B will be 30 if low, and 80 if high.
The probability of low demand is 0.6 and the probability of high demand is 0.4

Clearly if it was going to be high demand we would prefer A, but if it was going to be low demand we would prefer B.
However, usually we do not know what demand is going to be, and so if we make the decision on expected values we get an expected value for A of (20 x 0.6) + (100 x 0.4) = 52.
The expected value for B is (30 x 0.6) + (80 x 0.4) = 50

So…we would choose A and get an expected 52.

However……suppose that we can employ a market research company to find out for us in advance what the demand is going to be. If we know what the demand is going to be then we could then choose the best one. This is what we mean by perfect knowledge – knowing the outcome before we have to choose between A and B.

Obviously if we employ the research company, we don’t know in advance what they will find out (otherwise there would be no need to employ them) but whatever they find out about the demand will be correct.

The might come back and tell us demand will be high. If they do then we will choose A and get 100.
However they might come back and tell us demand will be low. If they do then we will choose B and get 30.

Since we know that the probability of high demand is 0.4, there is therefore a 0.4 probability that the research company will come back with that answer (and we will then get 100).
Similarly, there is a 0.6 probability that the research company come back and say it is low demand (and we will then get 30).

So, if we do employ the company, the expected return then will be (0.6 x 30) + (0.4 x 100) = 58.

Remember that without the company (and therefore without the advance knowledge) we would get an expected value of 52.

So…..using the company and getting perfect knowledge will get us an extra 6 (58 – 52).

The only problem is that the research company will be charging us for their services, and so the most we would be prepared to pay for it is anything up to the extra 6 that we will gain. The value of the perfect information in this example is 6.

No – they will only give us one reply.
However when you employ them you don’t know which reply they will give (otherwise you would not need to employ them!).
There is a 0.6 probability they will find out that demand is low, and a 0.4 probability they will find that it is high.
Once we know their reply then we can make our decision.