1.In a hospital-doctor matching problem, if some doctors apply as couples:

A. There always exists a stable matching, and the hospital proposing DA will identify one.

B.Theremay, not exita stable matching.

C.There always exists a stable matching, and the doctor proposing DA will identify one.

D. More than one answer is correct.

2.A search engine is selling 2 advertising slots/positions. Three advertisers are competing for these slots. Slot1generates 100 clicks per day. Slot 2 generates 50 clicks per day. The value of each click is $10for advertiser A, $7 for advertiser B, and$8 for advertiser C. Assume that the search engine uses VCG. Mark all the correct answers.

A. Advertiser Agents slot 1 and pays $8 per click

B. Advertiser Bgets slot 2and pays $8per click

C. Advertiser Bgets slot 2and pays $7per click

D. Advertiser Cgets slot 2and pays $7per click

3.Mark all the correct statements about school choice problems.

A. Deferred acceptance is guaranteed to achieve a stable matching.

B. Top trading cycles is guaranteed to achieve a stable matching.

C. Deferred acceptance is guaranteed to achieve an efficient matching.

D. Top trading cycles is guaranteed to achieve an efficient matching.

E. All students prefer the outcome of top trading cycles to the outcome of deferred acceptance.

F.All students prefer the outcome of deferred acceptance to the outcome of top trading cycles.