9781118041581

Bidder Strategies 685

and $360 thousand. Here, the common equilibrium bidding strategy is bi

(1/3)(300) (2/3)vi. In turn, competing bids range from $300 thousand to

$340 thousand. Therefore, the BCB distribution is given by: H(b) [(b 

300)/40]^2 ; this is graphed as the H curve in Figure 16.1.

Common Values and the Winner’s Curse

Frequently, bidders are uncertain about the “true” value of an item put up for

competitive bid. For instance, the United States periodically sells offshore oil

tracts via sealed-bid auctions. The value of any tract is highly uncertain, depend-

ing on whether oil is found, at what depth and at what cost, and future oil

prices. Except for differences in costs, the profit from the tract is likely to be

similar across firms. Thus, to a greater or lesser degree, the tract has a com-

mon valuefor all bidders. The difficulty is that this value is unknown.

In making its bid, typically the individual firm first will form an estimate of

the tract’s potential value. Obviously, this estimate will be subject to error, and

firms may hold very different estimates of value. How should a profit-maximizing

firm bid in this situation?

Figure 16.2 depicts bidding behavior when the item for bid has a common

unknown value. The true (but unknown) value is labeled V. Centered at V is

the distribution of possible bidder estimates (curve E). The figure depicts a

normal distribution of estimates. On average, estimates reflect the true value,

V, but there is considerable dispersion. Some buyers underestimate and others

overestimate the true value. The figure also depicts a typical distribution of

bids (curve B). Obviously, each bidder, seeking a profit, submits a bid well

below its estimate of value. This explains why the bid distribution is centered

well to the left of (i.e., below) the estimate distribution.

Here is an important observation to draw from Figure 16.2. A winning bid

drawn from the right tail of the bid distribution may exceed the true value of

the item. The shaded tail shows the portion of the distribution of bids that

exceeds the true value. For a bid in this region, the buyer is said to fall prey to

the winner’s curse.After the fact, the auction winner finds that the good

obtained is worth less than the price paid for it. The source of the winner’s

curse lies in the fact that the winning bidder has been too optimistic and has

grossly overestimated the good’s value. When the firm’s (upward) estimation

error exceeds its bid discount, it buys the good at a price greater than its value.

For instance, suppose the true value of the oil tract is $2 million, but the most

optimistic bidder believes it’s worth $3 million. Hoping to win the lease at a

profit, this firm bids $2.3 million (discounts its estimate by $.7 million) but still

ends up overpaying and experiencing a $.3 million loss on the tract.

From the bidder’s point of view, the key to avoiding the winner’s curse is

to recognize that the act of winning conveys information about the bidder’s

estimate relative to others. In all likelihood, winning means that the bidder

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