Concept of this assignment
The purpose of the two problems in this assignment is to
- validate your understanding of how to set up a decision tree,
- determine the best choice, and
- calculate the expected value of perfect information (EVPI) as an upper limit on the value of new information.
This assignment prepares you for the end-of-class quiz, which will include similar questions.
Problem 1
As head of the Traffic Department, you are planning a new system of traffic lights. Your experts are divided into two groups. One believes in theory A and one in theory B (A or B is true, not both). At present, you consider the two theories equally plausible. You have two options for your light system: systems X and Y.
If theory A is true and you adopt system X, then your payoff will be 1 with probability 0.8 and 0 with probability 0.2. If theory B is true and you adopt system X, then your payoff will be 1 with probability 0.1, and 0 with probability 0.9. Your payoff to system Y is 0.5.
You have a two-period time horizon. You can choose system Y now for the two periods, or you can experiment for the first period (i.e., use system X) and then choose a system for the second period depending on your payoff in period 1.
- Draw the decision tree. Label carefully.
- Put the payoffs
- Put the probabilities you can write down immediately on the appropriate branches.
- Explain how to compute the other probabilities.
- Assuming that you wish to maximize the expected value of the payoffs, what strategy should you follow?
Problem 2
Marian Haste is a painter under contract to paint the exterior of a house for $50,000. Unfortunately for her, the outside temperature may drop below freezing. If it does, the paint will not stick well and may peel off. The paint may also peel off even if it doesn’t freeze. Either way the peeling happens, Marian would have to repaint the house, at a cost of $30,000.
The weather forecast indicates a 60% chance of rain. Marian also believes there is a 1/3 chance the paint may peel if the rain freezes, but only a 10% chance if it does not. Her choices now are either to go ahead and paint or to defer it until it’s warm enough so it won’t possibly freeze. Deferring the job would require her to pay $8,000 in overtime and penalties.
- What would you advise Marian to do? (Should Marian Haste go ahead and repaint at leisure?)
- What is the most Marian should pay for better information about the weather?
