Winner's Curse
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The winner's curse is a phenomenon that may occur in
common value auction In common value auctions the value of the item for sale is identical amongst bidders, but bidders have different information about the item's value. This stands in contrast to a private value auction where each bidder's private valuation of the ite ...
s, where all bidders have the same (''
ex post References Notes References Further reading * * External links * {{Latin phrases E ...
'') value for an item but receive different private (''
ex ante The term (sometimes written or ) is a New Latin phrase meaning "before the event". In economics, ''ex-ante'' or notional demand refers to the desire for goods and services that is not backed by the ability to pay for those goods and servi ...
'') signals about this value and wherein the winner is the bidder with the most optimistic evaluation of the asset and therefore will tend to overestimate and overpay. Accordingly, the winner will be "cursed" in one of two ways: either the winning bid will exceed the value of the auctioned asset making the winner worse off in absolute terms, or the value of the asset will be less than the bidder anticipated, so the bidder may garner 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). The winner’s curse phenomenon was first addressed in 1971 by three Atlantic Richfield petroleum engineers who claimed that oil companies suffered unexpectedly low returns "year after year" in early
Outer Continental Shelf The Outer Continental Shelf (OCS) is a legally defined geographic feature of the United States. The OCS is the part of the internationally recognized continental shelf of the United States which does not fall under the jurisdictions of the ind ...
oil lease auctions. Outer Continental Shelf auctions are common value auctions, where the value of the oil in the ground is essentially the same to all bidders.


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 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 of the market value. The winner, then, is the bidder making the highest estimate. If we assume that the ''
average In colloquial, ordinary language, an average is a single number or value that best represents a set of data. The type of average taken as most typically representative of a list of numbers is the arithmetic mean the sum of the numbers divided by ...
'' 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 In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on ...
. We are interested in a bidder's
expected value In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informa ...
from the auction (the expected value of the item, minus 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, or placing a bid that is below their
ex ante The term (sometimes written or ) is a New Latin phrase meaning "before the event". In economics, ''ex-ante'' or notional demand refers to the desire for goods and services that is not backed by the ability to pay for those goods and servi ...
estimation of the value of the item for sale—but equal to their
ex post References Notes References Further reading * * External links * {{Latin phrases E ...
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 or 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 ''nth''
order statistic In statistics, the ''k''th order statistic of a statistical sample is equal to its ''k''th-smallest value. Together with Ranking (statistics), rank statistics, order statistics are among the most fundamental tools in non-parametric statistics and ...
, which increases as the number of bidders increases. There is often confusion that the 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 independently 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 recognizing an antique or other collectible 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 A petroleum reservoir or oil and gas reservoir is a subsurface accumulation of hydrocarbons contained in porous or fractured rock formations. Such reservoirs form when kerogen (ancient plant matter) is created in surrounding rock by the prese ...
. 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 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 for ...
s in which companies bid on licenses to use portions of the
electromagnetic spectrum The electromagnetic spectrum is the full range of electromagnetic radiation, organized by frequency or wavelength. The spectrum is divided into separate bands, with different names for the electromagnetic waves within each band. From low to high ...
. Here, the uncertainty would come from, for example, estimating the value of the cell phone market in
New York City New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive w ...
. *
IPO An initial public offering (IPO) or stock launch is a public offering in which shares of a company are sold to institutional investors and usually also to retail (individual) investors. An IPO is typically underwritten by one or more investment ...
s, in which bidders need to estimate what the
market value Market value or OMV (open market valuation) 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 t ...
of a company's
stock Stocks (also capital stock, or sometimes interchangeably, shares) consist of all the Share (finance), shares by which ownership of a corporation or company is divided. A single share of the stock means fractional ownership of the corporatio ...
will be. *
Pay per click Pay-per-click (PPC) is an internet advertising model used to drive traffic to websites, in which an advertiser pays a publisher (typically a search engine, website owner, or a network of websites) when the ad is clicked. This differs from more t ...
advertising online, in which advertisers gain higher ranking if they bid higher amounts per click from a search engine user. *Federal offshore oil leases: the term ''winner's curse'' was originated in a paper published in the ''Journal of Petroleum Technology'', volume 23, 1971, pages 641-653. The authors were Capen, Clapp & Campbell. *Free agency in professional sports.


Related uses

The term ''winner's curse'' is also used in statistics to refer to the
regression toward the mean In statistics, regression toward the mean (also called regression to the mean, reversion to the mean, and reversion to mediocrity) is the phenomenon where if one sample of a random variable is extreme, the next sampling of the same random var ...
phenomenon, particularly in
genome-wide association studies In genomics, a genome-wide association study (GWA study, or GWAS), is an observational study of a genome-wide set of genetic variants in different individuals to see if any variant is associated with a trait. GWA studies typically focus on assoc ...
and
epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and Risk factor (epidemiology), determinants of health and disease conditions in a defined population, and application of this knowledge to prevent dise ...
. 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 In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the ...
much larger than is likely to be seen in subsequent replication studies.


See also

*
Buyer's remorse Buyer's remorse is the sense of regret after having made a purchase. It is frequently associated with the purchase of an expensive item such as a vehicle or real estate. Buyer's remorse is thought to stem from cognitive dissonance, specifically ...
*
Wisdom of the crowd "Wisdom of the crowd" or "wisdom of the majority" expresses the notion that the collective opinion of a diverse and independent group of individuals (rather than that of a single expert) yields the best judgement. This concept, while not new to ...
* Proteus phenomenon *
War of attrition (game) In game theory, the war of attrition is a dynamic timing game in which players choose a time to stop, and fundamentally trade off the strategic gains from outlasting other players and the real costs expended with the passage of time. Its precise o ...
*
Pyrrhic victory A Pyrrhic victory ( ) is a victory that inflicts such a devastating toll on the victor that it is tantamount to defeat. Such a victory negates any true sense of achievement or damages long-term progress. The phrase originates from a quote from ...
*
Vickrey auction A Vickrey auction or sealed-bid second-price auction (SBSPA) is a type of sealed-bid auction. Bidders submit written bids without knowing the bid of the other people in the auction. The highest bidder wins but the price paid is the second-highest ...
*
Auction theory Auction theory is a branch of applied economics that deals with how bidders act in auctions and researches how the features of auctions Incentivisation, incentivise predictable outcomes. Auction theory is a tool used to inform the design of real- ...
*
Paul Milgrom Paul Robert Milgrom (born April 20, 1948) is an American economist. He is the Shirley and Leonard Ely Professor of Humanities and Sciences at the Stanford University School of Humanities and Sciences, a position he has held since 1987. He is a ...
*
Robert B. Wilson Robert Butler "Bob" Wilson, Jr. (born May 16, 1937) is an American economist who is the Adams Distinguished Professor of Management, Emeritus at Stanford University. He was jointly awarded the 2020 Nobel Memorial Prize in Economic Sciences, toge ...


References


Further reading

* * * * * *


External links


www.gametheory.net
— applet demonstrating the winner's curse.

— article explaining the winner's curse in the context of the
Google Google LLC (, ) is an American multinational corporation and technology company focusing on online advertising, search engine technology, cloud computing, computer software, quantum computing, e-commerce, consumer electronics, and artificial ...
IPO. {{Game theory Auction theory Curses