Winner's curse

Why does the bidder who wins a hard-fought auction so often wish they had lost it?

The obvious explanation is that people get carried away — the room heats up, egos engage, someone bids past their own judgement. That story is not wrong about human beings, but it fails the test that matters: the effect turns up among sober professionals bidding by sealed envelope after weeks of geology, and in laboratory experiments where there is no crowd and nothing to be excited about. Strip out every trace of emotion and the winner still tends to have paid too much.

So there must be something in the structure of an auction itself that punishes winning. What could it be?

First, separate two kinds of thing being sold. If I am bidding for a painting because I love it, its worth to me is mine alone — I know it exactly, and no one else's opinion can make me wrong. But an offshore oil tract, a construction contract, a company's future cash flows, a radio spectrum licence: these have one true value that is the same for everybody and known to nobody. Everyone in the room is estimating the same hidden number.

Now grant the bidders every virtue. Suppose nobody is optimistic, nobody is reckless, and each estimate is honest and unbiased — errors scatter in both directions and average out to exactly right across the room. Can anything still go wrong?

Ask who wins. The highest bidder does, and under any sensible rule the highest bidder is the one who estimated highest. But the highest of a set of unbiased estimates is not an unbiased estimate. It is the largest error in the upward direction, selected deliberately. The auction is a machine for finding the most over-optimistic person present and handing them the bill.

Take seven bidders whose estimates of a tract genuinely worth 100 come out at 79, 86, 93, 100, 107, 114 and 121. As a group they are perfect: those seven average to exactly 100. Bid your estimate and the winner pays 121 for something worth 100. Suppose everyone, having read this far, shades by ten — the winner still bids 111 and still loses eleven. The mistake is not the size of the shading. It is that the shading was chosen without asking the right question.

And what is the right question? Notice what winning tells you, and when it tells you. At the moment the hammer falls, you learn that six other people, looking at the same rocks, thought it was worth less than you did. That is powerful evidence about the number you were estimating — and it arrives one second after it could have been used. The disciplined bidder does the inference in advance: not "what do I think this is worth?" but "what would this be worth given that mine turns out to be the highest estimate in the room?" That conditional value is always lower, and bidding it is the cure.

Two things make the gap wider, and both run against instinct. The noisier the estimates, the further the top one sits above the truth. And the more bidders there are, the higher the maximum of their errors climbs — so the correct response to a crowded auction is to bid less aggressively, exactly when everyone feels the pull to bid more.

The idea was put into circulation in 1971 by three Atlantic Richfield engineers, Capen, Clapp and Campbell, who noticed that bids on the same offshore lease routinely differed several-fold between highest and lowest — direct evidence of enormously noisy estimates — and argued the industry had been systematically overpaying. Whether oil companies really earned sub-normal returns has been argued over ever since, with some later analyses finding returns close to normal, which would mean bidders had learned to shade. The laboratory version is not disputed: in classroom auctions for a jar of coins, the average estimate typically falls short of the true value while the average winning bid exceeds it.

Three clarifications worth keeping.

The curse is not "the winner pays more than everyone else". Of course they do; that is the definition of winning. The curse is paying more than the thing is worth — an absolute loss, not a relative one.

Nor is it irrationality in the usual sense. The mistake is precise and identifiable: failing to condition on an event you know will have occurred if you are the one paying. That is why experienced bidders can and do avoid it, and why the same person can be careful about geology and careless about inference.

And it needs a common value to bite. In a private-value auction — the painting you love — winning tells you only that others liked it less, which costs you nothing. Where the value is a mixture, as most real auctions are, the curse is present in proportion to the common part. The same shape appears wherever a selection rule picks the top of a noisy distribution: the candidate who interviews most impressively, the trial with the most striking result.

• How much to shade in practice, and why the answer depends on the number of rivals you expect rather than the number you can see.
• Why an ascending open auction, where you watch rivals drop out, can soften the curse that a sealed envelope hides.
• The same selection effect in science: why the most exciting first result is the one least likely to replicate.

Every term the collection defines is gathered in the glossary.