“In the presence of very risk-averse bidders, a person
selling her house in an auction will have a high expected profit by using a
first-price, sealedbid auction.” True or false? Explain your answer. U2.
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.
(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 other?
(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?