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Skills Check

Skills Check

Question 13.1

1. The adjusted winner procedure applies to

  1. only two-party disputes or disputes that can be recast as two-party disputes.
  2. either two-party or three-party disputes.
  3. n-party disputes for all n.

1.

a

Question 13.2

2. The starting point with the adjusted winner procedure is to have each side—independently and simultaneously—spread 100 points over the issues in such a way that it ________________________________.

2.

reflects the relative worth of each issue to that party

Question 13.3

3. The winner part of the name adjusted winner refers to the fact that

  1. each party initially “wins” (that is, is given) each issue on which he or she places more points than the other party.
  2. objects ultimately go to whichever party bid more.
  3. it is impossible for both parties to win with any fair-division scheme.

3.

a

Question 13.4

4. The adjusted part of the name adjusted winner refers to ______________.

4.

the transfer of items (or parts thereof) from one party to the other until points are equalized

Question 13.5

5. In transferring items from one party to the other with the adjusted winner procedure,

  1. the order in which items are transferred is extremely important.
  2. only one item will need to be split or shared.
  3. the order of transfer is obtained by looking at so-called point ratios.
  4. all of the above.

5.

d

Question 13.6

6. With the adjusted winner procedure, suppose A is the party with the highest point total. Then the fraction

A's point value of the itemB's point value of the item

is called the item's _____________________________.

6.

point ratio

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Question 13.7

7. With the adjusted winner procedure, the final allocation is

  1. equitable.
  2. envy-free.
  3. Pareto-optimal.
  4. all of the above.

7.

d

Question 13.8

8. With a fair-division procedure, if each player believes that he or she received the same fractional part of the total value, then the procedure is said to be ____________.

8.

equitable

Question 13.9

9. A fair-division procedure that produces an allocation with the property that no other allocation, achieved by any means whatsoever, can make any one player better off without making some other player worse off is said to be

  1. equitable.
  2. envy-free.
  3. Pareto-optimal.
  4. none of the above.

9.

c

Question 13.10

10. Chris and Terry must make a fair division of three objects. They assign points to the objects (as shown below) and use the adjusted winner procedure. Chris ends up with __________.

Object Chris Terry
Boat 30 20
Land 50 60
Car 20 20

10.

the boat, car, and part of the land

Question 13.11

11. In this chapter, the number of ways to generalize Knaster’s inheritance procedure from the case of a single object to the case of several objects is

  1. 0.
  2. 1.
  3. 2.
  4. 3.

11.

c

Question 13.12

12. The inheritance procedure that begins with each heir submitting a monetary bid for each object is known as ___________________________.

12.

The knaster inheritance procedure

Question 13.13

13. Chris and Terry use the Knaster inheritance procedure to divide a coin collection. Chris bids $1000 and Terry bids $800. What is the outcome?

  1. Chris gets the coins and pays Terry $200.
  2. Chris gets the coins and pays Terry $450.
  3. Chris gets the coins and pays Terry $500.

13.

b

Question 13.14

14. Four children bid on two objects (as shown in the table below). Using the Knaster inheritance procedure, Adam ends up with the _________________.

Object Adam Beth Carl Dietra
House $80,000 $75,000 $90,000 $60,000
Car $10,000 $12,000 $13,000 $15,000

14.

cash only

Question 13.15

15. With the procedure known as taking turns, the optimal strategy for players is called

  1. the sincere strategy.
  2. the bottom-up strategy.
  3. the top-down strategy.

15.

b

Question 13.16

16. With taking turns, we assume that a rational player will ____________________.

16.

never willingly choose his or her least-preferred item, and avoid wasting a choice on an item that he or she knows will remain available and can be chosen later.

Question 13.17

17. Two people use the divide-and-choose procedure to divide a field. Suppose that Jeff divides and Karen chooses. Which statement is true?

  1. Karen always believes she gets more than her fair share.
  2. Karen can guarantee that she always gets at least her fair share.
  3. Karen can possibly believe she gets less than her fair share.

17.

b

Question 13.18

18. A fair-division procedure is envy-free when each player believes that ___________________.

18.

no other player received more than he or she did

Question 13.19

19. Using the Steinhaus procedure for three players (lone divider), what happens if there is a single portion that is the only one approved of by both nondividers?

  1. One of the other portions is given to the divider.
  2. The two nondividers flip a coin to determine who receives the approved portion.
  3. All portions are returned to the cake, and a different person serves as the new divider.

19.

a

Question 13.20

20. Using the Steinhaus procedure for three players (lone divider), if the two nondividers approve different portions, then ___________________.

20.

each nondivider receives a portion that he or she has approved

Question 13.21

21. Using the Banach-Knaster procedure for three or more players (last diminisher), what happens to the first portion after each person has inspected and possibly trimmed it?

  1. The portion goes to the last person to approve the portion, whether or not it was trimmed.
  2. The portion goes to the last person to trim the portion.
  3. The portion goes to the first person to approve and not trim the portion.

21.

b

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Question 13.22

22. Using the Banach-Knaster procedure for three or more players (last diminisher), the player who receives the first portion _____________________________________________.

22.

leaves the game

Question 13.23

23. Using the Banach-Knaster procedure for three or more players (last diminisher), suppose that Scott initially cuts a piece and passes it among the other people, none of whom trims it. What happens next?

  1. Scott gets this piece.
  2. The last person who is handed the piece keeps it.
  3. The piece is returned to the cake, and someone else cuts a piece.

23.

a

Question 13.24

24. Using the Banach-Knaster procedure for three or more players (last diminisher), when only two people remain, ______________________________.

24.

they use the divide-and-choose procedure

Question 13.25

25. For the Selfridge-Conway procedure for three players, which of the following statements is true?

  1. Each of the three players has the opportunity to trim the portions if they appear to be unfair.
  2. Each player receives a portion that he or she believes to be exactly one-third of the total.
  3. The first player may believe that the third player received more than a fair share.

25.

c

Question 13.26

26. For the Selfridge-Conway procedure for three players, the player who will definitely not receive the trimmed piece in Stage 1 is ___________________________________.

26.

the first player

Question 13.27

27. An example of a proportional cake-division procedure is

  1. Steinhaus’s lone-divider procedure.
  2. the Banach-Knaster last-diminisher procedure.
  3. the Selfridge-Conway procedure.
  4. all of the above.

27.

d

Question 13.28

28. In a Vickrey auction, the winner is the highest bidd but he pays only ______________.

28.

the amount of the second-highest bid

Question 13.29

29. If the bids in a Vickrey auction are $40, $50, $85, and $90, the winner is the

  1. $90 bidder and he pays $90.
  2. $85 bidder and she pays $85.
  3. $90 bidder and he pays $85.
  4. $85 bidder and she pays $90.

29.

c

Question 13.30

30. The only person mentioned in this chapter in connection with two different fair-division procedures is ______________________________.

30.

Brønislaw Knaster

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