The following questions review the main ideas of this chapter. Write your answers to the...

The following questions review the main ideas of this chapter. Write your answers to the questions and then refer to the pages listed by number to make certain that you have mastered these ideas.

What kinds of items can be divided using the method of sealed bids? pg. 235 Why is it in a player’s best interest to make an honest bid? pgs. 235–236 What is a drawback of the method of sealed bids? pgs. 235–237

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Suppose that a brother and a sister have inherited a classic car from their grandfather in Missouri. Unfortunately, the brother lives on the Eastern seaboard and the sister lives on the Pacific coast. Geography dictates that one of them should be the sole owner of the car. Thus, one of them will get the car and will pay the other person an amount of cash worth half the value of the car. However, which sibling should buy out the other, and how should they determine the fair value of the car? If they decide first who is buying out whom, then it may be hard to set a fair price objectively. The person getting the car may claim its value is low, while the one giving up his or her share of the car may claim its value is high. Assuming that both siblings want the car and can afford to buy out the other, one fair way to set the price and decide who gets the car is illustrated in the following example.

Notice that the steps in the method of sealed bids differ somewhat from the procedure used in Example 4.5, in which we used the average of the two bids as the value of the car and determined the compensation due to Amanda based on that value. However, if we were to apply the method of sealed bids to Example 4.5, the result would be the same as in our earlier solution. Amanda gets half of her $2900 bid, or $1450. Blake pays $3100 to the fund and gets half of it, or $1550, back. That leaves $100 in the fund, which is split equally, leaving Amanda with $1500 and Blake paying only $1500; that is, Amanda would receive $1500 in monetary compensation, and, as high bidder, Blake would pay $1500 and receive the car. Keep in mind that no player will know in advance whether he or she is buying or selling each item, so each player is motivated to bid a fair price. It is in every player’s own best interest to make an honest bid. In the method of sealed bids, it is possible that one player could make the high bid on most items or even on every item and would end up compensating the other players. Therefore, to use this method, the players need to have enough cash to cover the possibility of buying out the other players’ shares. The next example shows how the method of sealed bids can be applied to the division of two items among three persons, each of whom has sufficient resources to buy out the others, if necessary.