Optimal Auctions 691reserve price, the good is withdrawn from sale.^16 A reserve price serves two
related purposes: It protects the seller from auctioning the good for too low a
price, and it potentially can elevate the final bid price. To see how a reserve
price works, let vsdenote the seller’s value (or reservation price) for the item
being sold. This reservation price could represent the personal value the seller
places on the item (e.g., the personal value for a painting). Alternatively, it
might represent a fallback price at which the seller knows she can sell the item
outside the auction. (For instance, the seller already may have been offered
$320,000 for the office building.) Clearly, the seller never should accept an
auction price below vs. In fact, one can show that the seller should set the
reserve price Pminto be strictly greater than her value; that is, Pmin vs. (This
is analogous to a seller demanding a price in excess of her reservation value in
the negotiation settings discussed in Chapter 15.) By setting such a reserve
price, the seller risks the possibility that the highest bid, bmaxwill not attain
Pmin, even when a mutually beneficial transaction exists, that is, when vsbmax
Pmin. The advantage of the reserve price is that it forces buyers to bid higher
than they otherwise might to meet the reserve.^17(^16) The reserve price may be public or silent. A public reserve is announced prior to the bidding and
establishes where the bidding starts. A silent reserve price is established by having a representative
of the auction house bid on the seller’s behalf up to the agreed-upon minimum. In either case, if
no buyer bids above the minimum, the item goes unsold and is returned to the seller.
(^17) When revenue equivalence holds, one can show that the English and sealed-bid auctions using
the right reserve price are optimal auctions; that is, each produces the maximum revenue of all pos-
sible auction procedures.
Besides traditional sales of antiques and artwork, auctions today are increas-
ingly used to sell items ranging from real estate to offshore oil leases to treas-
ury securities to inventories requiring liquidation. Intermediate goods are sold
on business-to-business auction exchanges. Online auctions at eBay, Yahoo,
and other sites have shown explosive growth. Google sets click prices for online
advertising using a variation of the second-price auction.
Does actual bidding behavior conform to the benchmark predictions pre-
sented in this chapter? Studies of real-world auction markets and the results of
controlled economic experiments provide a mixed answer. For instance, buy-
ers in English auctions (with private values) behave broadly as expected—bid-
ding up to their reservation prices if necessary. By contrast, in sealed-bid
auctions (also with private values), bids tend to be greater than the risk-neutral
equilibrium prediction. This is directly evident in controlled experiments using
volunteer subjects (usually undergraduate or MBA students or executive par-
ticipants). Even experienced subjects tend to bid too high (possibly due to risk
aversion) in attempting to win items up for sealed bids.
In common-value settings, elevated bids are the norm. While bids in English
and second-price auctions tend to be above the equilibrium benchmark, winning
Business Behavior:
Real-Life Bidding
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