Buying a Car: You plan on buying a used car. You have $12,000, and you are not eligible for any loans. The prices of available cars on the lot are given as follows:
For any given year,you prefer a Camry to an Impreza, an Impreza to a Corolla, a Corolla to a Civic, and a Civic to a LeSabre. For any given year, you are willing to pay up to $999 to move from any given car to the next preferred one. For example, if the price of a Corolla is $z, then you are willing to buy it rather than a Civic if the Civic costs more than $(z - 999), but you would prefer to buy the Civic if it costs less than this amount. Similarly you prefer the Civic at $z to a Corolla that costs more than $(z + 1000), but you prefer the Corolla if it costs less. For any given car, you are willing to move to a model a year older if it is cheaper by at least $500. For example, if the price of a 2003 Civic is $z, then you are willing to buy it rather than a 2002 Civic if the 2002 Civic costs more than $(z - 500), but you would prefer to buy the 2002 Civic if it costs less than this amount.
a. What is your set of possible alternatives?
b. What is your preference relation between the alternatives in (a) above?
c. Draw a decision tree and assign payoffs to the terminal nodes associated with the possible alternatives. What would you choose?
d. Can you draw a decision tree with different payoffs that represents the same problem?