Suppose that three risk-neutral bidders are interested in purchasing a Princess Beanie Baby. The bidders (numbered 1 through 3) have valuations of $12, $14, and $16, respectively. The bidders will compete in auctions as described in parts (a) through (d); in each case, bids can be made in $1 increments at any value from $5 to $25.
(a) Which bidder wins an open-outcry English auction? What are the final price paid and the profit to the winning bidder?
(b) Which bidder wins a second-price sealed-bid auction? What are the final price paid and the profit to the winning bidder? Contrast your answer here with that for part (a). What is the cause of the difference in profits in these two cases?
(c) In a sealed-bid first-price auction, all the bidders will bid a positive amount (at least $1) less than their true valuations. What is the likely outcome in this auction? Contrast your answer with those for parts (a) and (b). Does the seller of the Princess Beanie Baby have any clear reason to choose one of these auction mechanisms over the othed (d) Risk-averse bidders would reduce the shading of their bids in part (c); assume, for the purposes of this question, that they do not shade at all. If that were true, what would be the winning price (and profit for the bidder) in part (c)? Does the seller care about which type of auction she chooses? Why?