each other and that, for each buyer, values between $200,000 and
$260,000 are equally likely.
a. How should the renter decide whether or not to match the outside offer?
b. What offer should the outside buyer make if her value is $240,000? More
generally, what offer should she make as a function of her value, v?
c. What is the seller’s expected revenue? Confirm that it is lower than
under either the English or sealed-bid auctions.- Movie distributors sell films to local exhibitors via sealed competitive
bids. Exhibitors complain about the system of “blind” bidding—that is,
they are often forced to bid on a film sight unseen (before the film is
even completed). At the risk of oversimplifying, suppose a typical film
might be worth $10,000 per week (a hit), $6,000 (OK), or $2,000 (a
dog). Each of these outcomes is considered equally likely for the typical
unseen film.
a. Suppose three risk-neutral exhibitors are bidding for a film.
What is the expected value of the typical film under blind bidding?
In a sealed-bid auction where equilibrium bids are placed, what is
the distributor’s expected revenue from the competition? Could
the distributor increase its expected revenue by delaying the
bidding until after the film can be viewed (so its value will be
known)? Explain. How do your answers change if exhibitors are
risk averse?
b. Could a distributor increase its expected revenue by selectively
screening only its best films but making the bidding on the rest of
the films blind?
c. Suppose three exhibitors bid for a film after viewing it. Exhibitor A is
extremely astute and so can make a precise prediction of the film’s
value. Exhibitors B and C have only imprecise information about this
value. Could the distributor increase its expected revenue by
excluding one of the bidders? If so, which one? - Two buyers compete for an antique silver bowl in a sealed-bid auction.
Each buyer’s value is drawn independently from the range of $0 to
$1,000 with all values in the range equally likely. Buyer 1’s value for the
bowl is $700, and he submits a sealed bid of $280. Buyer 2 has the value
$450, makes a sealed bid of $300, and wins the bowl.
a. As profit maximizers, did the buyers make the appropriate sealed
bids? Did the “right” buyer get the bowl? Compute the sum of the
players’ payoffs (i.e., the seller’s revenue plus the winning buyer’s
profit).
b. What would have been the outcome (and total players’ payoffs) under
an English auction? Does the comparison of English and sealed-bid
prices contradict revenue equivalence? Which auction provides the
greater total “pie”?
700 Chapter 16 Auctions and Competitive Biddingc16AuctionsandCompetitiveBidding.qxd 9/26/11 1:09 PM Page 700