Imagine a jar of coins at a school fair. Everyone guesses how much is inside, and the highest bidder wins the jar for the price they bid. Nobody is biased. Some guess too high, some too low, and the average guess is exactly right. So why does the winner so often go home poorer than they came?
When the prize is worth the same to everyone, a jar of coins or a stretch of seabed that may hold oil, each bidder only has an estimate of that value. Estimates scatter around the truth. Now ask who wins. The bidder with the highest estimate. Winning an auction is not a random draw from the crowd. It is a filter that picks out the most optimistic error in the room.
That is the winner’s curse. The name comes from a 1971 paper, “Competitive Bidding in High Risk Situations,” in the Journal of Petroleum Technology, written by three employees of the oil company Arco: Ed Capen, Robert Clapp and William Campbell. They worried that oil companies’ winning bids for drilling leases were too high to leave a decent profit. The paper is usually credited with giving the effect its name.
There is a tidy piece of maths behind it. If each bidder’s error is equally likely to be anywhere between −S and +S euros, the highest of N errors is, on average, S × (N − 1) ÷ (N + 1) above the truth. With one bidder that is zero. With two it is a third of S. With twenty it is more than 90% of S. More bidders means a more extreme winner.
The prize below is secretly worth exactly €100. Each bidder gets a private estimate that is right on average, with errors up to the “noise” you set. Every bidder bids their estimate minus a “shave” that you also set. The highest bid wins and pays what it bid. Start with no shave, then press Run 1,000 auctions.
Two things to try. First, leave the shave at zero and drag the room from 2 bidders up to 20. The average of all estimates never moves from €100, yet the winner’s profit sinks, because a bigger crowd makes the top estimate more extreme. Second, raise the shave until the average winner’s profit reaches zero. For this simple room that happens at a shave of S × (N − 1) ÷ (N + 1), the same number as above. Shaving is not stinginess. It is correcting for the filter.
In the early 1980s the researchers Max Bazerman and William Samuelson auctioned jars worth $8.00 each to MBA students at Boston University: 48 auctions across 12 classes. The students’ average estimate of what a jar held was $5.13, which is too low. Even so, the average winning bid was $10.01, so the typical winner lost about $2.01. The winners were not fools about the jar. They forgot that being the winner told them something about themselves.
Later lab work by John Kagel and Dan Levin found the same pattern with a twist that matches the slider above: in larger groups, bidders lost money on average, while the theory says a careful bidder should have bid more cautiously as the group grew. Real bidders often did the opposite.
In the 1969 sale of drilling rights on Alaska’s North Slope, according to a review by the economist Richard Thaler, the winning bids added up to about $900 million, against about $370 million for the second-highest bids. A gap that large between first and second place is a sign that the winner’s estimate was an outlier.
The curse is not a law. It needs two ingredients: a prize with one true value that all bidders share, and estimates that are noisy. Remove either one and it fades. If you simply love a painting more than anyone else does, winning it says nothing bad about your estimate. If you have a better survey than your rivals, your errors are smaller, so the top estimate is closer to the truth.
The fix is a habit of thought: before you bid, ask “what would I believe about this prize if I knew mine was the highest estimate in the room?” The honest answer is “less than I do now.” That is the shave. The more bidders, the noisier your information, and the less you know about the prize, the bigger it should be. Slide the controls once more and watch the break-even number change with them.