2020 · Economics

The winner's curse, and the auction built to beat it

Q: In a common-value auction, why is the winner often the one who overpays?

Because the highest bidder is usually the one who most overestimated the shared value. When the true value is the same for everyone but uncertain, the winner is whoever guessed highest, and the highest guess is typically too high. That trap is the winner's curse.

Q: What is the difference between a private value and a common value?

A private value differs from bidder to bidder, while a common value is the same for everyone but unknown at bid time. A private value is personal, like how much you love a painting. A common value, like the oil under a field, is identical for whoever wins but uncertain when bids are placed, which is exactly what creates the winner's curse.

Q: Why did the Simultaneous Multiple Round Auction work so well for selling radio spectrum?

It offered every licence at once over many rounds, letting bidders learn from rising prices and re-optimise. By auctioning every licence simultaneously with prices that rise across rounds, the format lets bidders discover values, switch between licences, and tame the winner's curse, which is why it raised hundreds of millions where the airwaves had been almost free.

Awarded to Paul R. Milgrom and Robert B. Wilson “for improvements to auction theory and inventions of new auction formats”.

What was the 2020 Nobel Prize in Economics awarded for?

The 2020 Economics prize honours the people who explained why auction winners so often overpay, and who designed a new kind of auction to stop it. Robert Wilson showed that when an item's true value is uncertain but shared by everyone, the winner tends to be whoever overestimated it the most, the so-called winner's curse. Paul Milgrom extended the theory and, with Wilson, designed the multi-round format that the United States used in 1994 to sell radio spectrum, raising hundreds of millions where the airwaves had once been given away.

Predict first

A jar of coins is auctioned to a crowded room. Everyone guesses how much is inside and bids their guess, and the average guess is about right. Who tends to win, and what happens to them?

Whoever overguessed the most wins, and overpays. Because the true amount is the same for everyone, the winner is the person with the highest estimate, and the highest estimate is almost always too high. This trap is the winner's curse. Wilson showed that smart bidders see it coming and deliberately bid below their own best guess.

Predict first

You are selling one item to several bidders who are unsure what it is worth. Would you rather they bid once in secret, or call out rising prices in the open until all but one drop out? Which earns you more?

The open, rising auction usually earns more. As bidders drop out, everyone still in learns something about the item's value, so they grow less afraid of overpaying and bid higher. Milgrom proved that the more bidders learn about each other's valuations during the auction, the higher the seller's expected revenue.

In a common-value auction the winner is whoever overestimated the shared value the most, so winning means overpaying. When values are private and differ for each bidder, that trap disappears.

Imagine your class guesses how many jellybeans fill a big jar, and whoever guesses highest gets to buy the jar for the number they shouted. Nobody knows the real count. Some kids guess too low, some too high. The winner is always one of the kids who guessed way too high, so they pay more than the jar is worth. Winning actually makes them lose.

That trap has a name: the winner's curse. Two economists, Robert Wilson and Paul Milgrom, worked out exactly when it happens and how clever bidders dodge it, by guessing a little low on purpose.

The whole idea in one line

Good auctions let bidders learn

Milgrom and Wilson showed that an auction works best when bidders can watch and learn from each other while it runs. So they invented a new auction with many rounds, where prices climb slowly and everyone keeps learning. The United States used it in 1994 to sell the invisible radio waves that phones use, and it worked so well that countries around the world copied it.

Auctions split into two ideal types. In a private-value auction, an item is worth a different amount to each bidder, and what you would pay tells you nothing about what I would pay: think of a painting you simply love. In a common-value auction, the item is worth the same to everyone, but nobody knows that value for sure when they bid: think of the right to drill an oil field, where the amount of oil underground is identical whoever wins.

The winner's curse

Why winning can mean overpaying

In a common-value auction, every bidder forms a noisy estimate of the shared value. The winner is whoever estimated highest, and the highest estimate is usually an overestimate. So unless bidders correct for it, the act of winning is bad news: it tells you that you were the most over-optimistic person in the room. Wilson proved that rational bidders respond by shading their bids below their best estimate, and shade more when they are more uncertain or less informed than their rivals.

Paul Milgrom built a richer theory that mixes both kinds of value, since real auctions are almost always a blend. A telecom firm bidding for spectrum cares about a common value (how much the licence is worth to anyone) and a private value (its own costs and customer base). Milgrom, partly with Robert Weber, then asked which format the seller should choose.

How much bidders learn during the auction

More learning means less fear of the winner's curse, and usually higher prices for the seller.

Dutch auction (price falls until someone buys)almost none

The first action is the winning bid, so rivals reveal nothing on the way.

Sealed-bid auction (everyone bids once, in secret)none during bidding

English auction (price rises, bidders drop out)a lot

Each drop-out reveals a rival's limit, so survivors fear overpaying less and bid higher.

These insights pushed Milgrom and Wilson, with Preston McAfee, to design a new format for the hardest auction of all: selling thousands of interdependent radio-spectrum licences at the same time.

Wilson's common-value model is the canonical setting for the winner's curse. Each of n bidders draws a private signal of an unknown common value V. Conditional on winning a first-price auction, a bidder learns that their signal was the most optimistic of all, which is informative bad news. The Bayesian-rational response is to bid not on the naive estimate E[V | own signal] but on E[V | own signal is the highest], which is strictly lower. Wilson showed this shading deepens with the number of rivals and with the dispersion of signals, and that when one bidder is better informed, the disadvantaged bidders shade further or drop out.

Milgrom and Weber, the linkage principle

Why openness raises revenue

Milgrom and Weber's 1982 general model lets each bidder's value mix a private component with a common component correlated across bidders. Their central result, the linkage principle, ranks the standard formats by expected revenue: the more the price a winner pays is tied to information that surfaces during bidding, the higher the seller's expected revenue. Under affiliated values this gives the ordering English at least as good as second-price, which is at least as good as first-price and Dutch. The ascending English auction wins because public drop-out points correlate with the common value and partly neutralise the winner's curse.

Spectrum is the brutal case. Licences are neither pure private nor pure common value, and they are complements and substitutes at once: a carrier may need two adjacent regions together, or be indifferent between two bands. Auctioning licences one at a time forces each bidder to guess what they will later pay for the rest, creating exposure risk and inefficient allocations. Milgrom, Wilson and McAfee answered with the Simultaneous Multiple Round Auction (SMRA).

The SMRA mechanism

Many lots, many rounds, ascending prices

All licences are offered at once. In each round bidders submit fresh bids on any lots they want; afterwards the standing high bids and bidders are posted, and bidding continues until a full round passes with no new bid. Because prices rise gradually and information is public between rounds, bidders discover prices and re-optimise across lots, switching between substitutes and assembling complements while the winner's curse is held in check. Activity rules force bidders to stay active early, stopping them from hiding their demand until the end.

From theory to tens of billions

First use: in July 1994 the FCC sold 10 nationwide licences in 47 rounds for 617 million dollars, spectrum it had previously handed out almost for free.
Scale: FCC spectrum auctions using SMRA raised more than 120 billion dollars between 1994 and 2014, and the format has generated over 200 billion dollars worldwide.
Spread: Finland, India, Canada, Norway, Poland, Spain, the UK, Sweden and Germany adopted it, and it has also been used to sell electricity and natural gas.
Open frontier: SMRA can struggle when licences are strong complements, which motivated later designs such as the combinatorial clock auction (CCA).

Worth knowing

Airwaves once given away now worth over 200 billion dollars

Before 1994 the United States handed out radio-spectrum licences for almost nothing, through hearings and lotteries that speculators often gamed. After Milgrom, Wilson and Preston McAfee designed the multi-round auction, the very first sale raised 617 million dollars for ten licences, and the format went on to generate more than 200 billion dollars worldwide.

Check yourself

In a common-value auction, why is the winner often the one who overpays?

Why: When the true value is the same for everyone but uncertain, the winner is whoever guessed highest, and the highest guess is typically too high. That trap is the winner's curse.

What is the difference between a private value and a common value?

Why: A private value is personal, like how much you love a painting. A common value, like the oil under a field, is identical for whoever wins but uncertain when bids are placed, which is exactly what creates the winner's curse.

Why did the Simultaneous Multiple Round Auction work so well for selling radio spectrum?

Why: By auctioning every licence simultaneously with prices that rise across rounds, the format lets bidders discover values, switch between licences, and tame the winner's curse, which is why it raised hundreds of millions where the airwaves had been almost free.

Key terms

Winner's curse: In a common-value auction, the tendency for the winner to be whoever overestimated the shared value the most, and so to pay more than the item is worth.
Common-value auction: An auction where the item is worth the same to everyone, but its value is uncertain when bids are placed, like the right to drill an oil field.
Private-value auction: An auction where the item is worth a different amount to each bidder, so one bidder's value says nothing about another's.
Simultaneous Multiple Round Auction (SMRA): The format invented by Milgrom, Wilson and McAfee that offers many related lots at once over repeated rounds with ascending prices, letting bidders learn and re-optimise.
English auction: An open ascending auction where the price rises and bidders drop out one by one, revealing information that reduces the winner's curse.

The laureates

Paul R. Milgrom

Stanford University, Stanford, CA, USA

Born in Detroit in 1948, Milgrom built the more general theory of auctions, one that handles both common values (the same for everyone but unknown) and private values (different for each bidder). Working partly with Robert Weber, he showed which formats earn the seller the most and why an open ascending auction tames the winner's curse better than a sealed bid. With Wilson and Preston McAfee he then turned that theory into the SMRA format used to sell radio spectrum.

Photo: Eva Meyersson Milgrom, Public domain (via Wikimedia Commons)

Robert B. Wilson

Stanford University, Stanford, CA, USA

Born in 1937, Wilson was the first to build a framework for auctions of objects with a common value, a value that is unknown when bidding but turns out the same for everyone. In classic papers from the 1960s and 1970s he showed why rational bidders shade their bids below their own best estimate, to avoid the winner's curse of paying too much. His work laid the foundation that Milgrom later generalised.

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