2. (15 points)Which of the following auctions are DSIC? Clearly explain your
reasoning.

(a) (5 points)There are k identical items and n people. We choose the
tallest k people and take their bids. If their bid is greater than or
equal to \$5 we give them the item for a cost of \$5. If their bid is
lower than \$5 they don’t get the item.

(b) (5 points)Players in a single item auction buy ra✏e tickets for a dollar
each. At the end of the ra✏e a ticket number is drawn and the winner

(c) (5 points) Bidder’s valuations are independently distributed. A re-
serve price, ri, is set for the ith bidder so as to maximize revenue.

The highest bidder wins the auction and pays the second highest
price if he outbids the reserve price otherwise they don’t win.

3. DSIC Myerson’s Lemma

(19 points) The new Pokemon card packs are being released at Nintendo
stores across the nation for one day only. Di↵erent stores have a di↵er-
ent number of cards. There are n Pokemon fans that are interested in
purchasing the cards and the i
th fan has their own private valuation with
utility gain ui = xi(vi ! pi), where xi is the number of Pokemon cards
she receives, vi her valuation, and pi is her price per card. Due to social
distancing rules, only one fan will be allowed in the store on the release
day. Assume fans are only able to visit stores that are within 50 miles
of where they live and call the set of stores for fan i, Si. Suppose the
day before the release everyone submits a bid to Nintendo and they assign
them either no store or a store s 2 Si.

ALLOCATION RULE:

We order the fans 1, 2, 3,…,n where their bids are b1 >b2 >b3 > ··· >bn.

• We start with the highest bidder and continue down this line to the
next highest bidder.

• Fan i is sent to the store, s 2 Si, with the highest number of cards
in stock where no other fan has been assigned to yet. She is allowed
to buy as many cards as are available. If no store exists within ﬁfty
miles of fan i’s home, fan i is not assigned a store