PRACTICE EXAM QUESTIONS

**Fair shares:**

Give examples to show the following are wrong:

- In a fair division, everybody gets their favorite piece.
- In a fair division, everybody gets the same amount.
- Everybody agrees what splitting in half means.
- If a division is fair, nobody wants to trade.
- If everybody gets the same amount in the opinion of an impartial observer, it's fair.
- If everybody gets the same amount in their own opinion, it's fair.

Fill in a table of values, like on the worksheet.

Assign fair shares, like on the worksheet.

**I cut, you choose:**

The winning strategy for the divider in I cut, you choose is to
a) divide it into a good piece and a bad piece
b) divide it so that an impartial observer thinks he has cut it in half
c) divide it so that the other player says that both halves are equal
d) divide it so that both halves are equal in his own opinion

The winning strategy for the chooser:
a) Choose the smallest piece
b) Choose the piece that they themselves like best
c) Choose the piece the other person likes best
d) Choose the piece that an impartial observer thinks is best

Amy and Bob are trying to share two slices of cake, each of a different flavor
(Chocolate and Strawberry)  Amy likes chocolate twice as much as strawberry,
but doesn't know Bob's opinion.  How should she divide the cake to guarantee
she gets gets a fair share?

a) One portion is the chocolate slice, one portion the strawberry slice.
b) One portion is three quarters of the chocolate slice, and one portion is the rest.
c) One portion is half of the chocolate slice, and one portion is the rest.
d) There is no way to be sure she can get her fair share.
e) Cake is cake; it doesn't matter how she divides it.

Ch.3 #15 (p. 106)

**Lone divider:**

The winning strategy for the divider in Lone Divider among four players is:
a) Divide the goods into four equal parts (from the divider's point of view)
b) Divide the goods into four equal parts (according to an impartial observer)
c) Make his own piece larger, and stick everyone else with a smaller piece
d) The divider is not guaranteed a fair share

The winning strategy for each chooser in Lone Divider is:
a) Bid on only the best piece
b) Bid on all acceptable pieces
c) Bid on all pieces
d) The divider is in control; choosers are not guaranteed a fair share

Ch.3 #21 (p. 107)

**Lone chooser:**

Seven players already have their fair share, and a new player joins.
What is the winning strategy for each old player when dividing their portion?
a) Divide the goods into eight equal parts (from the divider's point of view)
b) Divide the goods into eight equal parts (according to an impartial observer)
c) Make one piece larger; with 56 pieces to examine, the new player won't notice
d) After the new player enters, they will no longer have their fair share

What is the winning strategy for the new player?
a) Choose the best piece from each old player
b) Choose smaller pieces from some players, larger from others
c) Take the largest seven pieces from the group, and rearrange the remaining ones fairly
d) There is no winning strategy; old players might divide unfairly

Ch.3 #33 (p. 109)

**Sealed bids:**

What is the winning strategy for the method of sealed bids?
a) Bid high; you will get more cash in the payout
b) Bid low; you will get the item for cheaper
c) Bid how much you think each item is worth
d) Sealed bids are inherently unfair

Ch.3 #53 (p. 114)