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?

How would your answers change to the above questions if the valuations of the sketch are $3.0, $2.7, $2.0 and $1.5?