1. In a hospital-doctor matching problem, if some doctors apply as couples [10 pts.]: A. There always exists a stable matching, and hospital proposing DA will identify one. B. There

may not exit a stable matching. C. There always exists a stable matching, and 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. Slot 1 generates 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 A gets slot 1 and pays $8 per click B. Advertiser B gets slot 2 and pays $8 per click C. Advertiser B gets slot 2 and pays $7 per click D. Advertiser C gets slot 2 and pays $7 per 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. 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. A. There always exists a stable matching, and hospital proposing DA will identify one.