Nobel Prize in Economics 2020: Auction Theory and New Auction Formats

This note covers the Nobel Prize in Economics 2020: who won it, why auctions are hard to analyse, how private-value and common-value auction theory works, how Paul Milgrom and Robert Wilson's ideas led to new auction formats such as the simultaneous multiple round auction for radio spectrum, how the discovery unfolded, why it matters, and quick facts for exams.

What was the Nobel Prize in Economics 2020 awarded for?

The official citation reads: "for improvements to auction theory and inventions of new auction formats".

This single sentence covers two linked achievements: first, building better theory to explain how bidders behave in different kinds of auctions, and second, turning that theory into practical auction designs that governments and companies could actually use.

In plain words, an auction is simply a way of selling something by letting buyers compete with bids.

The laureates worked out the mathematics of how rational bidders should behave when they do not know exactly what an item is worth, and then used that understanding to invent new ways of running auctions for complicated goods like radio frequencies, where the old methods did not work well.

The full official name of the award is the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, commonly called the Nobel Prize in Economics. It was announced on 12 October 2020 and carried a prize amount of 10,000,000 Swedish kronor, shared equally between the two winners.

Who are the laureates?

Paul R. Milgrom

Paul R. Milgrom was born on 20 April 1948 in Detroit, MI, USA. At the time of the award he was affiliated with Stanford University, Stanford, CA, USA, and he received one half of the prize.

Milgrom had earlier been Robert Wilson's doctoral student. He built a more general theory of auctions that allowed for both private values (a personal value that differs from bidder to bidder) and common values (a value that is, in the end, the same for everyone but uncertain beforehand).

He also showed how sellers could raise more revenue by sharing information with bidders, and he helped invent new real-world auction formats, including the format used by the US government to sell radio frequencies in 1994.

Robert B. Wilson

Robert B. Wilson was born on 16 May 1937 in Geneva, NE, USA. He too was affiliated with Stanford University at the time of the award, and he received the other one half of the prize.

Wilson developed the theory of auctions for objects with a common value, explaining why rational bidders tend to bid below their own best guess of that value, to protect themselves from what is called the winner's curse.

He later worked with Milgrom and Preston McAfee to design the simultaneous multiple round auction used for selling spectrum licences.

What problem were Milgrom and Wilson trying to solve?

People have sold goods to the highest bidder, or bought services from the cheapest offerer, for a very long time.

The press release notes that "objects worth astronomical sums of money change hands every day in auctions," covering everything from household items and art to securities, minerals, energy and public procurement contracts.

The scientific background document adds that the Greek historian Herodotus recorded auctions in ancient Babylon around 2,500 years ago, that Roman creditors used auctions to sell assets seized from debtors, and that Stockholms Auktionsverk, the world's oldest surviving auction house, was founded in 1674.

Sotheby's traces its own history to a 1744 book sale in London.

By the twentieth century, auctions had become central to selling government bonds, electricity, timber, minerals, petroleum and, crucially, radio frequencies used by mobile phone networks.

The trouble was that economists did not yet have a rigorous way to predict how bidders would behave, because an auction is not a simple either-or decision: each bidder must think strategically about what other bidders know and might do.

The Royal Swedish Academy of Sciences explained that analysing auctions properly only became possible after game theory itself had been extended beyond simple win-lose situations, work credited to earlier laureates such as John Nash, William Vickrey and John Harsanyi.

Milgrom and Wilson took this foundation and pushed it much further, eventually using their results to redesign real auctions used by governments. This is the background against which their 2020 prize was awarded.

How does auction theory work from the ground up?

Three things that decide an auction's outcome

The popular science background explains that any auction's result depends on three factors. The first is the format: are bids open or sealed, how many rounds are there, and does the winner pay their own bid or the second-highest bid? The second is the nature of the object: does each bidder value it differently (a private value), or do all bidders ultimately value it the same (a common value)? The third is uncertainty: what information do different bidders actually have about the object's true worth?

Four classic auction formats

Economists traditionally compared four formats:

1. The English auction: the price starts low and rises as bidders call out higher bids in the open; the last bidder standing wins and pays their final bid.
2. The Dutch auction: the price starts high and falls until a bidder agrees to buy at that price.
3. The first-price sealed-bid auction: bidders submit secret bids once, and the highest bidder wins and pays exactly what they bid.
4. The second-price sealed-bid (Vickrey) auction: bidders submit secret bids, the highest bidder wins, but pays only the second-highest bid.

William Vickrey, who won the Economics prize in 1996, had shown in the early 1960s that when bidders only have private values and are rational and risk-neutral, these four formats all give the seller the same expected revenue on average, a result known as the revenue-equivalence theorem.

Private values versus common values

A private value is personal: how much you enjoy a dinner with a celebrity does not depend on what anyone else thinks it is worth.

A common value is shared but uncertain, such as the amount of oil under a plot of land, or the future value of a radio-frequency licence: in the end there is one true value, but bidders only have imperfect estimates of it.

Definition: Winner's curse. In an auction with common values, the bidder who wins is often the one who most overestimated the item's true worth, so winning the auction can itself be a warning sign of having overpaid.

Robert Wilson showed mathematically that rational bidders, aware of this risk, deliberately bid below their own best estimate of the common value to protect themselves.

He also showed that greater uncertainty makes bidders more cautious, pushing final prices down, and that the problem grows worse when some bidders have better information than others.

Draw a horizontal line representing possible estimates of an object's true common value, mark the true value in the middle, then plot several bidders' individual guesses scattered around it; circle the highest guess to show that the auction winner is likely to be the bidder who overestimated the value by the largest amount.

How did Milgrom extend the theory and build new auction formats?

Combining private and common values

Most real auctions mix both types of value. Paul Milgrom, in a series of papers published around 1980, some written with Robert Weber, worked out a general theory covering both private and common values together.

He showed that an auction format earns the seller more revenue when the format allows bidders to learn more about each other's estimates as the bidding proceeds.

This explained, for example, why an English auction tends to raise more revenue than a Dutch auction: in the English format bidders see where others drop out and so gain information that reduces the winner's curse, encouraging more confident bidding; in the Dutch format no such information is revealed before the sale closes.

Milgrom's work also showed that sellers benefit from sharing expert appraisals, such as authenticity certificates or inspection reports, before bidding starts, because better-informed bidders bid more boldly, which raises the final price.

Why old methods for selling radio frequencies failed

From the 1990s, governments faced a new, harder problem: how to allocate interrelated objects such as radio-spectrum licences across many regions at once.

The popular science text describes how the United States originally used a beauty contest, where companies argued why they deserved a licence, which wasted money on lobbying and raised little revenue for the government.

This was replaced by random lotteries, which left mobile networks fragmented across regions and triggered a second-hand market where speculators profited instead of taxpayers.

The simultaneous multiple round auction

In 1993 the United States decided frequency bands would instead be sold through auctions. Milgrom and Wilson, working partly with Preston McAfee, invented the Simultaneous Multiple Round Auction (SMRA), in which all licences across every region are offered at the same time, with low starting prices and repeated bidding rounds that let bidders learn about demand and adjust, reducing uncertainty and the winner's curse.

The steps of how an SMRA typically proceeds, as described in the sources, were:

1. The regulator opens bidding on all the interrelated licences at once, starting from low prices.
2. Bidders place bids across multiple licences simultaneously in each round.
3. Results of each round are revealed, letting bidders see roughly where demand is strongest.
4. Bidding continues in further rounds, with prices rising on contested licences.
5. The auction closes once no bidder wants to raise any bid further, and licences go to the final highest bidders.

When the US Federal Communications Commission (FCC) first used an SMRA in July 1994, it sold 10 licences over 47 bidding rounds, raising 617 million US dollars in total, for licences the government had previously handed out almost free of charge.

Many other countries, including Finland, India, Canada, Norway, Poland, Spain, the UK, Sweden and Germany, later adopted the same format, and the source states that the FCC's own auctions using this method brought in more than 120 billion dollars between 1994 and 2014, with over 200 billion dollars raised worldwide from spectrum sales using this approach.

Milgrom later helped develop further refinements, including the Combinatorial Clock Auction, which lets bidders bid on packages of several frequencies together rather than one at a time, and the two-round Incentive Auction, where spectrum is first bought back from existing holders and then resold to operators who can use it more efficiently.

How did the discovery unfold?

Why does it matter?

The Nobel committee stated that the laureates' discoveries "have benefitted sellers, buyers and taxpayers around the world." Auctions now determine the price of electricity, carbon emission allowances, financial securities, fishing quotas and government bonds, not only traditional goods like art and farm produce.

The prize committee's chair, Peter Fredriksson, was quoted as saying this year's laureates "started out with fundamental theory and later used their results in practical applications, which have spread globally," calling their discoveries "of great benefit to society." This case is notable because the same researchers developed both the basic theory and the real-world designs that used it, which the scientific background called an unusually direct example of basic research leading to invention.

Open questions remain about designing auctions for even more complex situations, such as preventing collusion between bidders in auctions of interrelated objects, and balancing a government's wish for revenue against the goal of allocating resources efficiently. Researchers continue to refine formats like the Combinatorial Clock Auction to address these challenges.

How does this connect to what you study?

Auction theory builds directly on game theory, the branch of economics that studies how people make decisions when the outcome depends on what others do, and students meet this idea whenever they study strategic behaviour in markets.

The idea of a common value that is uncertain in advance, such as the amount of minerals under a plot of land, connects to how students learn about scarce natural resources and how governments decide who gets to use them.

The story of how the United States moved from beauty contests to lotteries and finally to auctions for radio frequencies is a clear, real example of how public policy can change when an older method fails, which links to civics topics on how governments allocate public resources and raise revenue through methods like spectrum sales, bond auctions and public procurement contracts.

Students studying demand, supply and market design will recognise auctions as a real mechanism through which prices are actually set in markets for electricity, government bonds and emission allowances, rather than only an assumption drawn as a simple textbook diagram.

Quick facts for exams

The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2020, widely called the Nobel Prize in Economics, was awarded jointly to Paul R. Milgrom and Robert B. Wilson, both of Stanford University, USA.

"for improvements to auction theory and inventions of new auction formats." The announcement was made on 12 October 2020 by the Royal Swedish Academy of Sciences, and the prize carried an amount of 10,000,000 Swedish kronor, split equally between the two laureates.

Wilson worked out the theory of common-value auctions and the winner's curse, while Milgrom generalised this to cover both private and common values and co-designed the Simultaneous Multiple Round Auction used worldwide for spectrum sales, first by the US Federal Communications Commission in 1994.

Note: Source. The prize facts in this note are from the Nobel Prize's official site, nobelprize.org.

Glossary

• Auction — a method of selling or buying where participants compete by submitting bids, and the format's rules decide the winner and price.
• Auction format — the specific rules of an auction: how bids are made, how prices change, and how the winner and price are decided.
• Private value — the value of an item that differs from bidder to bidder and does not depend on other bidders' opinions.
• Common value — a value that is ultimately the same for all bidders but uncertain in advance, such as the amount of oil in a reserve.
• Winner's curse — the tendency for the auction winner in a common-value auction to have overestimated the item's true worth.
• English auction — an open auction where the price rises until only one bidder remains, who pays their final bid.
• Dutch auction — an auction where the price starts high and falls until a bidder accepts it.
• First-price sealed-bid auction — bidders submit one secret bid; the highest bidder wins and pays exactly that bid.
• Second-price (Vickrey) auction — bidders submit secret bids; the highest bidder wins but pays the second-highest bid.
• Revenue-equivalence theorem — Vickrey's result that several standard auction formats give the seller the same expected revenue under private values, provided bidders are rational and risk-neutral.
• Linkage principle — the idea that an auction format earns more revenue when its final price reflects more of the bidders' private information.
• Simultaneous Multiple Round Auction (SMRA) — a format selling many related licences together across repeated bidding rounds, invented for US spectrum sales.
• Combinatorial Clock Auction — an auction letting bidders bid for packages of several related items together.
• Incentive Auction — a two-round format where spectrum is bought back from current holders and resold to more efficient users.
• Beauty contest (licensing) — an older method of allocating licences by argument rather than bidding, replaced because it encouraged costly lobbying.

Common errors and misconceptions

• Misconception: Auction theory only applies to art and antiques. Correct: The sources describe auctions used for securities, minerals, energy, radio frequencies, government bonds and public procurement.
• Misconception: The winner's curse means the auction winner always loses money. Correct: It means winners are likely to have overestimated the true value, which can reduce their profit, not necessarily cause an outright loss.
• Misconception: Milgrom and Wilson only did theoretical work. Correct: They also designed real auction formats, including the SMRA used by the FCC in 1994.
• Misconception: All four classic auction formats always give different revenue. Correct: Under private values and rational, risk-neutral bidders, Vickrey showed they give the same expected revenue, the revenue-equivalence theorem.
• Misconception: Common value and private value are the only two possibilities in any auction. Correct: Most real auctions mix both elements together, which Milgrom's general theory specifically addressed.
• Misconception: Spectrum licences were always sold by auction in the USA. Correct: The USA first used beauty contests, then lotteries, before adopting auctions from 1993 onward.
• Misconception: Only Robert Wilson studied the winner's curse. Correct: Wilson first identified and analysed it formally, but Milgrom's later work also addressed how different formats worsen or reduce it.

Exam-style questions with model answers

Q1. Who were the joint winners of the Nobel Prize in Economics 2020, and what was their joint citation? [2 marks]

1. Paul R. Milgrom and Robert B. Wilson won the prize jointly, for improvements to auction theory and inventions of new auction formats, as stated in the official citation.

Q2. Define the winner's curse and explain why it occurs in common-value auctions. [3 marks]

1. The winner's curse is the tendency for the bidder who wins a common-value auction to have overestimated the item's true shared worth.
2. Because each bidder only has an imperfect private estimate of the common value, the bidder with the most optimistic estimate tends to bid highest and win.
3. Since the winner's estimate was the highest among all bidders, it is likely to have been an overestimate, meaning the winner may have paid more than the item's true value.

Q3. Explain, in 3 to 4 sentences, why the English auction tends to generate higher revenue than the Dutch auction when values have a common component. [4 marks]

1. In an English auction, the price rises openly, and bidders can observe when other bidders drop out, which reveals information about those bidders' private estimates.
2. This revealed information lets remaining bidders update and reduce their fear of the winner's curse, so they bid more confidently and the price can climb higher.
3. In a Dutch auction, the price falls until someone accepts, and no information about other bidders' estimates is revealed before the sale closes.
4. Because less information is shared, bidders in a Dutch auction protect themselves by bidding more cautiously, which the linkage principle identifies as leading to lower expected revenue for the seller.

Q4. Describe the problems with the earlier methods used to allocate radio-frequency licences in the United States, and how the Simultaneous Multiple Round Auction solved them. [5 marks]

1. The United States initially allocated frequency licences through a beauty contest, where companies argued their case for deserving a licence, which encouraged heavy spending on lobbying and raised little revenue.
2. This was replaced with random lotteries, which left national mobile operators with fragmented networks across different regions and created a large second-hand market where speculators, rather than the government, captured the value of licences.
3. As the national debt grew, it became politically difficult to keep giving away licences worth billions of dollars for almost nothing, so in 1993 the United States decided to use auctions instead.
4. Milgrom and Wilson, working with Preston McAfee, invented the Simultaneous Multiple Round Auction, which offered all the interrelated geographic licences together, starting from low prices with repeated bidding rounds.
5. This design reduced uncertainty and the winner's curse because bidders could learn about demand across rounds, and when first used in July 1994 it sold 10 licences in 47 rounds for 617 million dollars, far more than previous methods had raised; the format was later adopted by many other countries.

Q5. What is the difference between a private value and a common value in auction theory? [2 marks]

1. A private value is personal to each bidder and does not depend on other bidders' opinions, while a common value is ultimately the same for everyone but uncertain in advance of the auction.

Q6. Outline Paul Milgrom's main contribution to auction theory beyond Robert Wilson's earlier work. [4 marks]

1. Robert Wilson had analysed the special case of pure common-value auctions, explaining the winner's curse when bidders share one uncertain true value.
2. Paul Milgrom, in papers published around 1980, developed a more general theory that allowed for both private and common value elements together, which better matches most real auctions.
3. He showed that an auction format gives the seller higher expected revenue when it allows bidders to learn more about each other's estimated values as bidding proceeds.
4. He also showed that sellers benefit from sharing expert appraisals of an object with bidders before an auction, since better-informed bidders bid more confidently and the final price rises.

Key takeaways

• Milgrom and Wilson shared the Economics prize 2020 for improving auction theory and inventing new auction formats.
• Robert Wilson developed the theory of common-value auctions and was the first to formally describe the winner's curse.
• Paul Milgrom generalised the theory to cover both private and common values together, and introduced the linkage principle.
• The Simultaneous Multiple Round Auction, co-invented by both laureates with Preston McAfee, was first used by the US FCC in 1994.
• Many countries around the world later adopted similar simultaneous auction formats to sell their own radio-spectrum licences.
• Both laureates were affiliated with Stanford University in the United States at the time the prize was awarded.
• The prize committee praised the pair for moving from fundamental theory to practical, globally used auction applications.
• Open challenges remain in designing auctions that prevent bidder collusion in complex, interrelated, multi-object sales.

Test yourself

What was the official citation for the Economics Nobel Prize 2020?

The citation was "for improvements to auction theory and inventions of new auction formats," awarded jointly to Milgrom and Wilson.

Where was Paul Milgrom affiliated at the time of the award?

Paul Milgrom was affiliated with Stanford University, Stanford, CA, USA, at the time of the award.

What is the winner's curse?

The winner's curse is the tendency for the winning bidder in a common-value auction to have overestimated the item's true worth.

Which new auction format did Milgrom and Wilson help design for spectrum sales?

They helped design the Simultaneous Multiple Round Auction, first used by the US Federal Communications Commission in 1994.

What method did the United States first use to allocate radio-frequency licences, before auctions?

The United States first used a beauty contest, where companies argued their case, and later switched to random lotteries.

Why does an English auction often raise more revenue than a Dutch auction under common values?

The English auction reveals information as bidders drop out, reducing the winner's curse and encouraging more confident, higher bidding.

Who proved the revenue-equivalence theorem, and what does it state?

William Vickrey proved it, showing that under private values and rational bidders, several standard auction formats give the seller the same expected revenue.