Suppose there are 3 risk-neutral bidders that are interested in purchasing a Pablo Picasso painting at an auction. The bidders have valuations for the painting of $8 million, $10 million, and $15 million. The bidders do not know each other's valuations. Bids can be in thousand dollar increments.
a) For each of the three auctions listed below, explain which bidder will win, what will be the final bid-price that is paid to the seller, and what will be the final profits for each of the three bidders. Fully explain your answers and any assumptions you make.
i) Open-cry English auction
ii) Second-price sealed-bid Vickery auction
iii) First-price sealed-bid auction
b) Contrast your answers for the three auctions. Fully explain what the cause of any differences was.
c) If you were the seller of the Picasso painting, which auction would you prefer? Explain.