You are considering auctioning a Leonardo Da Vinci original sketch. You entice four bidders to come to your auction. The bidders' valuations of the sketch in decreasing order are $3.0, $2.2, $2.0, and $1.5 (in millions).

• If you used a second-price sealed bid auction, who would win and what would the winning price be?

• If you used a first-price sealed bid auction and the optimal strategy for the participants was to shade their bid by 20% and the participants used this strategy, who would win and what would the winning price be?

• Which auction should you choose to maximize your profit? The first-price bidders shade their bids by 20% of their evaluation of its value. The second-price bidders all utilize the optimal strategy for second price auctions stated in the textbook.

Answer the above questions if the valuations of the sketch are $3.0, $2.2, $2.0 and $1.5.