"The used car buyer problem"

It was first proposed in:

R. A. Howard, “The used car buyer", in Readings on the Principles and Applications of Decision Analysis (R. A. Howard and J. E. Matheson, eds.), pp. 689–718, Menlo Park, CA: Strategic De-

cisions Group, 1984.

And it has been described in many papers. It is described in Shenoy (2000) as follows:

"Joe is considering buying a used car from a dealer for $1000. The market price of similar cars with no defects is $1100. Joe is uncertain whether the particular car he is considering is a "peach" or a "lemon". Of the 10 major subsystems in the car, a peach has a serious defect in only one subsystem, whereas a lemon has a serious defect in six subsystems. The probability that the used car under consideration is a lemon is 0.2. The cost of repairing one defect is $40, and the cost of repairing six defects is $200.

For an additional $60, Joe can buy the car from the dealer with an "anti-lemon guarantee". The anti-lemon guarantee will normally pay for 50% of the repair cost, but if the car is a lemon, then the guarantee will pay 100% of the repair cost.

Before buying the car, Joe has the option of having the car examined by a mechanic for an hour. In this time period, the mechanic offers three alternatives, t1 , t2 , and t3 as follows:

t1 : Test the steering subsystem alone at a cost of $9;

t2 : Test the fuel and electrical subsystems for a total cost of $13;

t3 : Do a two-test sequence in which Joe can authorize a second test after the result of the first test is known. In this alternative, the mechanic will first test the transmission subsystem at a cost of $10 and report the results to Joe. If Joe approves, the mechanic will then proceed to test the di?erential subsystem at an additional cost of $4.

All tests are guaranteed to find a defect in the subsystems if a defect exists. We assume that Joe's utility for profit is linear in dollars."

We have adopted the probabilities used in Smith et al. (1993) and Qi et al. (1994).