Tuesday, April 8, 2008

Damaged Goods: Another Guessing Game

Jackie and Greg, returning from a Las Vegas, find that the airline has damaged the identical antiques that each had purchased. An airline manager says that he is happy to compensate them but is handicapped by being clueless about the value of these strange objects. Simply asking the travelers for the price is hopeless, he figures, for they will inflate it.

Instead he devised a more complicated scheme. He asks each of them to write down the price of the antique as any dollar integer between 2 and 100 without conferring together. If both write the same number, he will take that to be the true price, and he will pay each of them that amount. But if they write different numbers, he will assume that the lower one is the actual price and that the person writing the higher number is cheating. In that case, he will pay both of them the lower number along with a bonus and a penalty—the person who wrote the lower number will get $2 more as a reward for honesty and the one who wrote the higher number will get $2 less as a punishment. For instance, if Jackie writes 46 and Greg writes 100, Jackie will get $48, and Greg will get $44.

What numbers will Jackie and Greg write? What number would you write?

2 comments:

Travis Kraker said...

Jackie and Greg, if they are honest people will write down the price that they paid for their items. However, since each person probably purchased these items at a different place then they probably each paid a different amount. Therefore, it is not quite fair in the airlines manager to do this since they each paid different prices for their item. I would put down 100 dollars for each item. I would do this in hopes that the other would think the same way. That way each price would be the same and we could each maximize our profits from this ordeal.

Lang said...

They will write as low as possible maybe 0. I will write 100 for each.