As a young boy in York, Nebraska, Stanford economist Robert Wilson and his friends would sometimes attend Saturday morning cattle auctions held near his childhood home and watch the farm animals get 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,” recalls 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 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 have studied.
Together, the pair have explored how different auction designs can yield different outcomes, and specifically, the role — 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 says. In other words, the winning bidder loses out and gets stuck paying more than the item is actually worth.
This phenomenon is what economist call the winner’s curse. Throughout the 1960s and 1970s, Wilson examined how the winner’s curse unfolded and 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 have if they’d known 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 had survey estimates for how much oil and gas could be extracted from a certain area, no one was entirely certain how much was below ground.
“To be inside the company and see how they did it was actually startling,” Wilson recalls. “I had no idea how bad their information was.” Furthermore, the future price of oil and gas is also incredibly volatile, he noted.
Here, Wilson was able to put economic theory to practice. He honed the concept of common value, known also as the mineral-rights model: Although each bidder has their private estimate 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. Milgrom later enriched the model to allow for both common and private values.
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.
It was 1993, and by that time, Milgrom, who’d come 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. That’s because bidders gain more information about an item’s value as the bidding process progresses, Milgrom found, and the more information bidders have about an object’s value, the higher the revenue.
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 — 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 recalls. “You bring in the first license, and da-da-da-boom, it’s sold and now you go to the next one, and the next one, and the next one. But that can make it really difficult [for a bidder] 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.” Between rounds, 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 are also imposed to help ensure auctions run smoothly and fairly. The auction ends 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 the fishing industry has turned to auctions as a way to reallocate fishing quotas — in New South Wales when fishermen want to retire, they didn’t want to sell one or two rights to catch fish, they wanted to sell all their rights as a bundle, Milgrom points out.
“In general, there are many auctions that occur in a 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,” Milgrom says. “It has to take into account how they interact in the whole system.”
Auctions as Collaboration
While there are other ways to allocate goods, like lotteries, they don’t guarantee that the items will go to people who need it most. Applications, or “beauty contests,” wherein participants make their case for why they are deserving, can be susceptible to corporate lobbying and interests — which happened to the FCC prior to their adoption of the SMRA method.
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,” says 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, 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 about the perceived shortage in respirators and other equipment.
“Well, there was not a shortage in respirators,” says 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 notes. “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 Holmström, who now teaches at the Massachusetts Institute of Technology and was awarded the Nobel in 2016 for his work on contract design.
It was through Holmström that Milgrom came to study under Wilson. In the 1970s, Milgrom and Holmström were classmates at Stanford, so when Milgrom decided to pursue his PhD, he asked Holmström for advice.
“He said, ‘You should get Bob Wilson to be your advisor,’” Milgrom recalls. 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 says. He recalls 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?” asks Milgrom.
Milgrom and Wilson have sought out more fundamental explanations. 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?,” Wilson asks. “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.”
As Wilson adds, scholarship is about advancing knowledge beyond the established set of concepts, research methods, and theories that are foundational in an academic field. These paradigms, he says, “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.”
This story was originally published on October 12, 2020 at Stanford News.