Winner's curse
Encyclopedia
The winner's curse is a phenomenon akin to a Pyrrhic victory
Pyrrhic victory
A Pyrrhic victory is a victory with such a devastating cost to the victor that it carries the implication that another such victory will ultimately cause defeat.-Origin:...

that occurs in common value auction
Common value auction
A common value auction is a term in economics used to describe an environment in which information about the value of the object for sale is dispersed among bidders. The term is used in different ways by different people. By one definition it describes an auction in which the good being auctioned...

s with incomplete information. In short, the winner's curse says that in such an auction, the winner will tend to overpay. The winner may overpay or be "cursed" in one of two ways: 1) the winning bid exceeds the value of the auctioned asset such that the winner is worse off in absolute terms; or 2) the value of the asset is less than the bidder anticipated, so the bidder may still have a net gain but will be worse off than anticipated. However, an actual overpayment will generally occur only if the winner fails to account for the winner's curse when bidding (an outcome that, according to the revenue equivalence theorem, need never occur). So despite its dire-sounding name, the winner's curse does not necessarily have ill effects in practice.

## Related uses

The term winner's curse is also used in a related but distinct sense in science, in particular genome-wide association studies. In studies involving many tests on one sample of the full population, the consequent stringent standards for significance make it likely that the first person to report a significant test (the winner) will also report an effect size
Effect size
In statistics, an effect size is a measure of the strength of the relationship between two variables in a statistical population, or a sample-based estimate of that quantity...

much larger than is likely to be seen in subsequent replication
Replication
Replication may refer to:Science* Replication is one of the main principles of the scientific method, a.k.a. reproducibility** Replication , the repetition of a test or complete experiment...

studies.

## Explanation

In a common value auction, the auctioned item is of roughly equal value to all bidders, but the bidders don't know the item's market value when they bid. Each player independently estimates the value of the item before bidding.

The winner of an auction is, of course, the bidder who submits the highest bid. Since the auctioned item is worth roughly the same to all bidders, they are distinguished only by their respective estimates. The winner, then, is the bidder making the highest estimate. If we assume that the average
Average
In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set. Average is one form of central tendency. Not all central tendencies should be considered definitions of average....

bid is accurate, then the highest bidder overestimates the item's value. Thus, the auction's winner is likely to overpay.

More formally, this result is obtained using conditional expectation
Conditional expectation
In probability theory, a conditional expectation is the expected value of a real random variable with respect to a conditional probability distribution....

. We are interested in a bidder's expected value
Expected value
In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...

from the auction (the expected value of the item, less than the expected price) conditioned on the assumption that the bidder wins the auction. It turns out that for a bidder's true estimate the expected value is negative, meaning that on average the winning bidder is overpaying.

Savvy bidders will avoid the winner's curse by bid shading
In an auction, bid shading describes the practice of a bidder placing a bid that is below what they believe a good is worth.Bid shading is used for one of two purposes. In a common value auction with incomplete information, bid shading is used to compensate for the winner's curse...

, or placing a bid that is below their ex ante estimation of the value of the item for sale — but equal to their ex post belief about the value of the item, given that they win the auction. The key point is that winning the auction is bad news about the value of the item for the winner. It means that he/she was the most optimistic and if bidders are correct in their estimations on average, that too much was paid. Therefore savvy bidders revise their ex ante estimations downwards to take account of this effect.

The severity of the winner's curse increases with the number of bidders. This is because the more bidders, the more likely it is that some of them have overestimated the auctioned item's value. In technical terms, the winner's expected estimate is the value of the first order statistic
Order statistic
In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value. Together with rank statistics, order statistics are among the most fundamental tools in non-parametric statistics and inference....

, which increases as the number of bidders increases. In other words, more bidders = higher winner's curse.

There is often confusion that winner's curse applies to the winners of all auctions. However, it is worth repeating here that for auctions with private value (i.e. when the item is desired independent of its value in the market), winner's curse does not arise. Similarly there may be occasions when the average bid is too low relative to exterior market conditions e.g. a dealer recognising an antique or other collectable as highly saleable elsewhere when other bidders do not have the necessary expertise.

## Examples

Since most auctions involve at least some amount of common value, and some degree of uncertainty about that common value, the winner's curse is an important phenomenon.

In the 1950s, when the term winner's curse was first coined, there was no accurate method to estimate the potential value of an offshore oil field
Oil field
An oil field is a region with an abundance of oil wells extracting petroleum from below ground. Because the oil reservoirs typically extend over a large area, possibly several hundred kilometres across, full exploitation entails multiple wells scattered across the area...

. So if, for example, an oil field had an actual intrinsic value of \$10 million, oil companies might guess its value to be anywhere from \$5 million to \$20 million. The company who wrongly estimated at \$20 million and placed a bid at that level would win the auction, and later find that it was not worth as much.

Other auctions where the winner's curse is significant:
• Spectrum auction
Spectrum auction
A spectrum auction is a process whereby a government uses an auction system to sell the rights to transmit signals over specific bands of the electromagnetic spectrum and to assign scarce spectrum resources. Depending on the specific auction format used, a spectrum auction can last from a single...

s in which companies bid on licenses to use portions of the electromagnetic spectrum
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....

. Here, the uncertainty would come from, for example, estimating the value of the cell phone market in New York City
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...

.
• IPO
Initial public offering
An initial public offering or stock market launch, is the first sale of stock by a private company to the public. It can be used by either small or large companies to raise expansion capital and become publicly traded enterprises...

s, in which bidders need to estimate what the market value
Market value
Market value is the price at which an asset would trade in a competitive auction setting. Market value is often used interchangeably with open market value, fair value or fair market value, although these terms have distinct definitions in different standards, and may differ in some...

of a company's stock
Stock
The capital stock of a business entity represents the original capital paid into or invested in the business by its founders. It serves as a security for the creditors of a business since it cannot be withdrawn to the detriment of the creditors...

will be.
• Pay per click
Pay per click
Pay per click is an Internet advertising model used to direct traffic to websites, where advertisers pay the publisher when the ad is clicked. With search engines, advertisers typically bid on keyword phrases relevant to their target market...

advertising online, in which advertisers gain higher ranking if they bid higher amounts per click from a search engine user.

• War of attrition (game)
War of attrition (game)
In game theory, the war of attrition is a model of aggression in which two contestants compete for a resource of value V by persisting while constantly accumulating costs over the time t that the contest lasts. The model was originally formulated by John Maynard Smith, a mixed evolutionary stable...

• No-win situation
No-win situation
A no-win situation, also called a "lose-lose" situation, is one where a person has choices, but no choice leads to a net gain. For example, if an executioner offers the condemned the choice of dying by being hanged, shot, or poisoned, since all choices lead to death, the condemned is in a no-win...

• Win-win situation
• Mexican standoff
Mexican standoff
A Mexican standoff is a slang term defined as a stalemate or impasse; a confrontation that neither side can foreseeably win. The term is most often used in lieu of "stalemate" when the confrontational situation is exceptionally dangerous for all parties involved.In popular culture, the Mexican...

• Pyrrhic victory
Pyrrhic victory
A Pyrrhic victory is a victory with such a devastating cost to the victor that it carries the implication that another such victory will ultimately cause defeat.-Origin:...

• www.gametheory.net — applet demonstrating the winner's curse.
• www.techcentralstation.com — article explaining the winner's curse in the context of the Google