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to its original estimate. Against more rivals, the buyer should bid more con-

servatively, not more aggressively.^12

FINAL NOTE When the item up for bid has a common but uncertain value,

bidding at an English auction becomes more subtle and complex than in a pri-

vate, independent value setting. Because of winner’s curse considerations, the

bidder cannot simply plan to bid up to its value estimate. Observing the num-

ber of active bidders and when they drop out conveys information about com-

petitors’ estimates and, therefore, the item’s unknown value. Thus, the buyer’s

upper bid limit should incorporate these observations.

(^12) The computation of conditional values and equilibrium sealed-bidding strategies is quite com-
plicated and thus is not pursued here.
CHECK
STATION 4
In a sealed-bid auction, you are uncertain about the value of an item up for bid, believ-
ing that the value is between $3,000 and $4,000. You expect to bid against a single rival
whom you realize is much more knowledgeable about the item’s value. In fact, your rival
can perfectly predict the item’s market value (i.e., knows the precise value between
$3,000 and $4,000). You are thinking of bidding $3,300 for the item. Assess the poten-
tial profitability as well as the potential risks of this bid.

OPTIMAL AUCTIONS

Earlier in this chapter, we noted the advantages of competitive bidding rela-

tive to posted prices and negotiated prices. We again take the perspective of the

auctioning party—a seller who is interested in maximizing the revenue from an

auction sale or a buyer who seeks the best terms (including minimum cost)

from a competitive procurement.

Expected Auction Revenue

What are the expected-revenue consequences of different types of auctions?

Which type of auction generates maximum expected revenue? In answering these

questions, it is convenient to restrict attention to the two most common auctions:

the English and sealed-bid auctions. Consider once again the symmetric, private-

value model, in which buyer values are drawn independently from the same dis-

tribution. For this setting, we can state the following remarkable result:

Suppose that the private-value model holds and that risk-neutral buyers adopt equi-

librium bidding strategies. Then the English, sealed-bid, Dutch, and Vickrey auc-

tions all generate identical expected revenues.

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