The bid picture: Nobel prize winners explain auction theory, collaboration

Robert Wilson and Paul Milgrom on the morning of Oct. 12, the day they received

Robert Wilson and Paul Milgrom on the morning of Oct. 12, the day they received the 2020 Nobel Memorial Prize in Economic Sciences (Image credit: Andrew Brodhead)

If designed correctly, auctions can distribute resources fairly, according to Stanford economists Robert Wilson and Paul Milgrom. The pair were awarded the 2020 Nobel Memorial Prize in Economic Sciences for their improvements to auction theory and inventions of new auction formats.

As a young boy in York, Nebraska, Stanford economist Robert Wilson and his friends would sometimes go watch the Saturday morning cattle auctions held near his childhood home and watch the farm animals be sold off, one by one.

"Us kids would just go over and sit in the bleachers. A cow would be pulled in and stand there while an oral, ascending auction of subsequent bids was conducted until the auctioneer declared the cow sold," recalled Wilson, whose scholarship in auction theory and design earned him and his Stanford colleague and former graduate student Paul Milgrom the 2020 Nobel Memorial Prize in Economic Sciences.

Wilson didn’t know it then, but the types of auctions he witnessed as a child are what economists call an English auction. These are the kinds of auctions most of us are familiar with, as they’re used to sell everything from artwork and antiques to memorabilia, but they’re only one among many auction designs that Wilson and Milgrom studied.

Together, the pair have explored how different auction designs can yield different outcomes, and specifically, the role information - or lack thereof - can play in shaping a buyer’s bidding strategy.

For example, in a cattle auction, each buyer knows how much beef they may get from a steer - they know if they fatten him up they could get somewhere between 400 to 500 pounds of retail cuts. But suppose there is great uncertainty about the price of beef. How much buck should the buyer bid for his bovine then?

For Wilson, that’s where things can get interesting and, in some cases, problematic.

"If different bidders have different information about what that price will be, then the person that overestimates the value the most will tend to win," he said. In other words, the winning bidder loses out and gets stuck paying more than the item is actually worth.

This phenomenon is what economists call the winner’s curse. Throughout the 1960s and 1970s, Wilson examined how the winner’s curse unfolded. He also learned that there are some instances where it makes buyers risk-averse: they are so worried by it that they end up bidding less than what they would if they knew the item’s true value.

It was while consulting with the Department of Interior on their auctions for mineral extraction rights and later, directly with oil companies, that Wilson saw firsthand some of the problems bidders encountered: While oil companies may have survey estimates for how much oil and gas could be extracted in a certain area, no one is entirely certain how much is below ground.

"To be inside the company and see how they did it was actually startling because I had no idea how bad their information was," Wilson recalled. Furthermore, the future price of oil and gas is also incredibly volatile, he noted.

Here, Wilson was able to apply economic theory to practice. He honed the concept of common value, known also as the mineral-rights model: while each bidder has his or her own private estimates of an item’s value, in the end, it is worth the same for everyone. In a common-value setting, each bid provides a glimpse into what the item is worth, and as the auction proceeds, bidders may adjust their estimates.

Up until that point, scholarship on auction theory had focused on private value models, that is, what an item is worth depends solely on the bidder’s assessment. Wilson’s contribution allowed auction theory to be applied in new settings and later, Milgrom enriched the model further to allow for both common and private values.

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The Royal Swedish Academy of Sciences cited the pair for improvements to auction theory and inventions of new auction formats.

Designing new auctions

When the United States Federal Communications Commission (FCC) wanted a new way to allocate licenses to the broadcast spectrum used for wireless communications, they reached out to Milgrom and Wilson for ideas.

Main auction types

Here, Stanford PhD candidate Mitchell Watt explains how auction formats can differ:

Auction formats differ in two key ways: the bidder’s information at the time of bidding and the price that the winner pays for the item.

In ’clock auctions’, like the English and Dutch auctions, the item’s price ticks up or down (Dutch) and everyone knows at all times which bidders are interested in the item. In contrast, bidders in ’sealed bid auctions’ place their bids into an envelope and only find out if they have won the auction at the end.

In term of payments, some auctions are ’first-price’ which means the winner pays their own bid, others are ’second-price’ which means the winner pays the second-highest bid and some are even ’all-pay’ which means every bidder must pay their bid, even if they don’t win the auction.

The auction format often depends on the setting. For example, houses are often sold using an English auction, flowers are sold in the Netherlands according to the Dutch auction and internet advertising slots are often sold using second-price sealed bid auctions.

It was 1993 and by that time, Milgrom, who came to study auctions at Stanford because of Wilson, was a professor himself. Milgrom had already conducted his own work in auction theory and design, including the discovery that English auctions - where bidding starts low and prices go up - are better at mitigating the winner’s curse than Dutch auctions - where bidding starts high and prices go down. The reason is because bidders gain more information about an item’s value during the bidding process and the more information bidders have about an object’s value, the higher the revenue, Milgrom found.

So, the FCC approached the pair to see if they could find a system that could deal with the problems they faced. For example, say a mobile phone carrier wanted coverage in California, they would have to buy licenses in both Southern and Northern California. But in some of the auction proposals that were put forth, there was a risk that a company could initially spend so much money on the Southern California license that they couldn’t afford the Northern California license later in the auction. That’s because the Southern and the Northern California licenses are worth more in combination than individually.

"In the initial proposals that were made to the FCC, they were just going to auction licenses off like a cattle auction," Wilson recalled. "You bring in the first license, and da da da - boom, it’s sold and now you go next to the next one, and the next one, and the next one. But that can make it really difficult to assemble a good package of licenses to get the kind of coverage that you want."

Milgrom and Wilson’s solution was elegant: What if the auction sold licenses all at once?

In their novel design - called the simultaneous multiple round auctions (SMRA) - all items are put up for sale at once and buyers can bid on any subset of items. Bidding is done in rounds where bidders discreetly place their bids at the same time. At the end of each round, all bids are revealed, providing bidders with information about the license’s value while ensuring that the license goes to whoever values it the most.

Because bidding is done in rounds, it mitigates the risk of "winner’s curse." Bidders also have time to reevaluate their strategies with any new insights they’ve gleaned from other buyers in the previous round.

In order to discourage bidders from sitting out a round, the auction also imposes an "activity rule" where bidders must make credible bids every round. Penalties for withdrawing a bid were also imposed to help ensure auctions ran smoothly and fairly. Auctions ended when no new bids are made on any of the items. The FCC adopted Milgrom and Wilson’s design almost in its entirety.

Their novel format became the basis for many other spectrum auctions across the world. Canada, Finland, Germany, India, Norway, Poland, Spain, Sweden and the U.K. have all used different versions of it.

Milgrom has also advanced other auction designs that have been adopted by other sectors. For example, electricity companies have used auctions to sell power during peak periods. Even fishing industries have turned to auctions as a way to reallocate fishing quotas - in New South Wales when fisherman wanted to leave the industry, they didn’t want to sell one or two rights to catch fish, they wanted to sell all their rights as a bundle, Milgrom pointed out.

"In general, there are many auctions that occur in the world where there are lots of things interacting and the auction can’t be just a one-by-one purchase or sale of any individual piece. It has to take into account how they interact in the whole system," Milgrom said.

Auctions as collaboration

While there are other ways to allocate goods, like lotteries, it is not a guarantee it will go to people who need it most. Applications, or "beauty contests," are another method where participants make their case for why they are deserving, but those can be susceptible to corporate lobbying and interests - which happened to the FCC prior to their adoption of the SMRA method.

Stanford economists Paul Milgrom and Robert Wilson win the Nobel in economic sciences

The Royal Swedish Academy of Sciences cited the pair for improvements to auction theory and inventions of new auction formats.

If designed correctly, auctions can distribute resources fairly, according to Wilson and Milgrom.

"People tend to have the impression that auctions are all about competition, but a lot of what we also study is how to design the rules to get an efficient, cooperative outcome," said Wilson.

An efficient outcome, according to economists, is one that maximizes the total welfare of those who are affected by a decision. In an auction, this includes not just the bidders themselves but also the auctioneer and other parties who might be affected by the auction’s outcome.

Take the distribution of medical supplies, for example, an issue that was important at the onset of the COVID-19 pandemic when there was serious concern among hospitals, patients and the general public alike about the perceived shortage in respirators and other equipment.

"Well there was not a shortage in respirators," said Milgrom. "The problem was that places in California were stockpiling respirators to make sure we had them when we needed them. But New York needs them today, we need them tomorrow. There is no reason why we can’t both have them, provided we have a good system for trading."

And the trading doesn’t have to involve money, Milgrom noted. "It could be a system that incorporates trading rights to use respirators tomorrow for rights to use respirators today - so that everyone is on an equal footing."

Economists call these matching markets - a theory advanced famously by Alvin Roth, another Stanford economist and former disciple of Wilson’s - who used this mathematical approach to match organ donors with recipients and medical residents with hospitals. This work earned Roth the Nobel Memorial Prize in Economics in 2012 .

’What’s the magic?’

Indeed, three of Wilson’s students have won the Nobel award: Roth, Milgrom and Bengt Holmstrom, who now teaches at the Massachusetts Institute of Technology and was awarded the Nobel in 2016 for his work on contract design.

Advice to aspiring scholars

What advice do Wilson and Milgrom have for scholars early in their career?

Robert Wilson:

"One piece of advice would be if you are going to be doing theoretical work make sure it’s strongly motivated by connections to practical things. Be involved in the real world and use that as the stimulus for your research.

"My own path was to get involved in very practical things and from those practical problems create some theory, do some basic research that addresses these problems that you find when you are dealing with something practical.

"For me, the consulting I did was really very educational. I learned so much and, based on my experience in these consulting relationships, I could then formulate problems that I could address in my basic research."

Paul Milgrom:

"I try to do the same thing that I attribute to Bob. I try to be encouraging to them, I try to point them towards good problems and I also try to encourage them to collaborate. Part of it is simply trying to get a good problem you are excited about, but I am trying to create a relationship among my students that makes more than the sum of the parts.

"Research is a collaborative endeavor. If you can bring people together who support each other, people who are serious about doing good work and excited about what they are doing, you can make amazing things happen."

It was through Holmstrom that Milgrom came to study under Wilson. In the 1970s, Milgrom and Holmstrom were classmates at Stanford, so when Milgrom decided to pursue his PhD, he asked Holmstrom for advice.

"He said, ’you should get Bob Wilson to be your advisor,’" Milgrom recalled. To get Wilson’s attention, Milgrom wrote a term paper on auction theory and the rest, as they say, is history.

So what makes Wilson such a special, sought-after mentor and, given the track record of his students’ accomplishments, a successful one at that?

"Part of that answer is that he was encouraging and he has great taste in problems. He would discourage us from working on things that were either intractable or didn’t matter," Milgrom said. He recalled how Wilson would ask him, "’Why would you even do that? Suppose you solve that problem, who is going to care?’"

Combining application with foundational research has been a defining feature of Wilson’s own career.

Both Wilson and Milgrom’s scholarship have questioned widely held beliefs, including some of the most fundamental principles of economics - like the model of supply and demand. This long-established theory posits that the more goods and services there are in the market, the lower its value is and vice versa, the smaller the amount, the higher the price.

"But how did that happen, what was the magic?" asked Milgrom.

Milgrom and Wilson have both sought out more fundamental explanations why. Both have used game theory to study the strategic interactions among decision-makers to provide foundations for the model of supply and demand in markets, including auctions.

"It’s true, in an auction maybe there is a demand curve and a supply curve and they intersect and that’s the price but how did that come about? It came about through the bidding strategies of the participants and the auction design and then we can question whether the price formation is incorporating the information in the right way," Wilson said.

As Wilson added further, scholarship is about advancing knowledge beyond the established set of concepts, research methods and theories that are foundational in an academic field. These paradigms, Wilson said, "are very dangerous because they make you blind to what’s going on inside. The thing to do is to go beyond the standard paradigm and look inside to what is really going on in greater detail."


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