Paul Milgrom, price discoverer and Nobel laureate

Joshua Gans 15 November 2020

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One thing I remember clearly about Paul Milgrom as an advisor is the child-like glee he would exhibit when he had found a new and interesting problem to solve. That happened one day in 1993 when he had been asked to consult on the proposal by the US Federal Communications Commission (FCC) to auction off spectrum for the next generation of mobile phones.

Congress had rejected the old idea of allocating spectrum by lottery or by some sort of beauty contest. Instead, telecommunications networks would have to bid for those rights so that the entity most willing to put their money where their mouth was would end up getting those valuable property rights. And like any government policy, they weren’t only interested in the money they might raise but ensuring that the spectrum was actually put to efficient use thereafter.

There was reason to be concerned. Other countries – notably New Zealand and Australia – had earlier embraced using auctions to allocate rights to publicly-owned assets. But as outlined by John McMillan (1994), policymakers had taken ‘off the shelf’ auctions and not previously tried auctions such as the second-price sealed-bid auction, and things had not gone well. The big problems were both in terms of implementation – details really mattered – and political – how did it all look in the end? 

Could these issues have been anticipated? On the one hand, what governments were trying to do was very well defined and in those cases, this is what the textbooks were saying. On the other hand, it is always more complex than that. When you have one-off events with lots of money on the table, market participants will apply themselves to think about how they can profit from it. To be sure, that is precisely what you are trying to encourage by having a market process. But if you are running an auction and you want all to go well, you have to ‘front-run’ that behaviour. 

Experience in 1993 now suggested that auction designers would have to up their game for the coming spectrum auction. Many economists, including Paul, were unlisted by various parties into the process. And it wouldn’t be easy. While the rights previously auctioned were ‘simple’, for mobile phone spectrum, there was a big challenge: the potential bidders had very different visions for the industry. 

One set of bidders were looking to augment regional mobile phone networks. This may seem odd today where we take the ability to use our phones worldwide for granted but as the industry started, even country-wide usage in the US was a luxury item. Those regional networks were intent on continuing that plan. 

The other set of bidders were looking to build out a nation-wide network. This meant that they would only be interested in regional spectrum if they could assemble and package it into national coverage. The FCC wanted to ensure they had a chance. But they were stuck. Auction the items using separate auctions and you might drive away national network builders who didn’t want to risk being stuck with regional spectrum that they couldn’t use. Bundle all of the regional rights together into national ones and the regional carriers would be out. Either way, you would be losing potential bidders and that would serve neither the FCC’s revenue nor efficiency objectives.

It was this conundrum that had landed on Paul’s desk, and he was energised. I was employed as a research assistant on that project. My rule was to find stuff out, particularly about things that had been tried in the past. But before I could get my work done, in what I remember was lightning speed, Paul told me that he and, his advisor, Bob Wilson, had cracked the puzzle. They would tell the FCC that it would be possible to have their cake and eat it too. But it would take patience and a new, unproven auction design: the simultaneous ascending bid auction.

The groundwork

Before describing the auction, it is important to move back a decade or so earlier when the genesis of what appears to have motivated Paul throughout his career emerged. Back in the 1970s, two important developments in economics occurred. The first was the abandonment by general equilibrium theorists of the question of trying to explain how prices emerged. The second was the rise of game theory.

Economists had always been obsessed with the role of prices. Prices could guide economic activity and efficient resource allocation. But at the same time, economists did not really know where prices came from. In the end, they had settled for the idea that prices are what they are because they are the prices that do the job.

This is a somewhat unfair, if kind of accurate, statement. In working out how prices move from disequilibrium to equilibrium, economists had to abandon their usual grounding of choices (in this case, the choice of a price) in economic rationality and instead rely on adjustment rules or ‘tatonnement’ (as it called by Leon Walras at the turn of the 20th century). And even those didn’t work so well. Somehow, the economy, untroubled by this, soldiered on. 

Game theory took another stab at the issue: prices should reflect the information of atomistic actors in the economy (as Frederick von Hayek had famously argued) so they would build a theory of price formation from the group up, starting with people who had different bits of information.

This resulted in the mechanism design approach of Leo Hurwicz but then ground to another halt with the impossibility theorems of Myerson and Satterthwaite (1983), which cast doubts on the ability of prices (even flexibly construed) to aggregate information of strategic agents in a way that produced efficient outcomes. Grossman and Stiglitz (1980) had found that you just couldn’t get an equilibrium under these conditions.

For Paul, however, how the market found its prices endured as a question. Rather than trying for a general approach, inspired by the work of William Vickery, he would build. And that starting point was where you could see prices being formed: auctions – places where many people come together with very conflicting agendas, they agree to a set of rules, a game is played, and then someone may end up reallocating a resource to another person for a clear price.

Vickrey (1961) had studied different ways that auctions were set up and found that when you just had one good being sold, to people who might have their own distinct values on owning that good, the three main auctions out there ended up with the same outcome. And to that, he added a fourth – a beauty of economic design called the second-price sealed-bid auction that no one but an economist could have come up with – and found that would do no better.

To get to that point, Vickrey had taken everything really interesting out of the environment he studied. In particular, the bidders did not look like anyone in the real world. When I value an item, like a house, I have my own distinct preferences for that house. But a house is also an asset. So, while my own preferences could explain about 10% of my willingness to pay for a given house, the remainder is driven by factors that are common across all buyers. What’s more, that gives me a clue to the value of my fellow bidders but not access to any particular insight they might have on those common elements.

This would mean, as Bob Wilson, so accurately characterised it, that the winner on those auctions is likely to be those who are the most optimistic. So while being pessimistic about the common value of an item might cause you to miss out in the fray, being optimistic causes you to come out on top. But what do you know? The winner is kind of the most wrong. And for rational bidders, they know that and so become more cautious. For someone designing an auction, this is a big problem. 

The bid conundrum

To economists, prices were the data of economic activity but a sideshow. To game theorists, the bids were messages sent by people to be interpreted and used. Apparently, it was only ordinary people who cared about the prices themselves. 

This was reflected in the related field of industrial organisation. In the early 1980s, several economists had argued that even a monopolist could act like a competitive firm because of the threat of entry. This was the theory of contestable markets. The idea was that faced with potential entry, a monopolist would engage in limit pricing and set their price just below the costs it would take for an entrant to come in and ‘outbid’ them for customers. 

Game theorists substantively critiqued that notion. Why should a monopolist ‘give away’ all of those profits just to signal to a potential entrant to stay away? Instead, they could just set high prices and then beat an entrant senseless should it come to that. And if entry were even slightly costly, why would anyone choose to do that (Dasgupta and Stiglitz 1988). 

Paul and his eventual long-time collaborator John Roberts had an answer to that: a bid can signal just how tough that competition might be. After all, an entrant might try it on if they believed the monopolist was slack and inefficient. This gave the monopolist and incentive to assuage those beliefs. Just saying so, wasn’t going to be persuasive (Milgrom and Roberts 1986). Instead, they would have to put their money where their mouth was – in a bid. Thus, limit pricing was a means by which monopolists could prove to would-be entrants their competitive strength (Milgrom and Roberts 1982).

To model auctions, bids had to be seen as signals and to be seen as signals, they had to be commitments. You couldn’t just name a bid without having to pony up with the money. Even during the process of getting to a price, you would need skin in the game. Auction rules had to be designed to ensure that happened. They couldn’t just ‘work’ in equilibrium. They had to work along the way.

Armed with this charge, Milgrom and his then co-author Robert Weber tackled the messy real-world leap that Vickrey had started. In so doing, they broaden the scope of what economists could tell us about whether auctions work well beyond the mere textbook and to the real world where they could have actual application. And you can see this from their Econometrica paper (Milgrom and Weber 1982) considered a high point of high theory in this area, which starts with applications of selling oil and gas rights before getting to any formal theory. 

What they found is that the process of price discovery mattered. In this general setting, the Dutch and first-price sealed-bid auctions came to the same outcome. But when bidders had different information, the same could not be said of the English or ascending bid auction and the second-price auction. In the English auction, you could see what other bids were along the way. That information proved very useful to bidders in updating their prices and avoiding the winner’s curse. The idea is that you wanted to link the prices that bidders ended up paying as closely as possible to the bids (or information going into the bids) of each other. The journey matters in terms of the endpoint. 

That paper was a tour de force. It provided a manual for auction designers well ahead of when that would become an industry. And so it was not surprising that when the US government wanted to run the largest auction in history, there was a ring on Paul Milgrom’s doorbell. 

An economic invention

For all the advances from Milgrom and Weber (1982), the spectrum auction was at a whole other level. It involved multiple assets with differing patterns of substitutability (you only want one package of spectrum in an area) and complementarity (you might want spectrum across areas). There was no clear information and there was considerable uncertainty about the evolution of the industry. Add to that a lot of money on the table and resolving these issues would be difficult.

The academic literature had left economists with clues but had also killed aspiration. There would be no perfect auction that could encourage buyers to bid their unfiltered willingness to pay. Instead, there would be gaming, uncertainty and potential mess. But the auction rules could guide and, in some cases, force outcomes that could improve matters.

Paul’s experience in delving into the messy details of auctions along with a life-long exploration of price discovery, had left him with intuition. He had a grounded sense of what was important and what was not. He also had a clarity of thought that gave him the ability to persuade in ways to which most economists can only aspire. And he wasn’t afraid of complexity. There was no retreat to, well, you’ll have to accept this bad outcome. Instead, there was hope that better was possible without letting the perfect be the enemy of the good.

In other fields, scientists invent things. Economics is not known for that. Economists study the world. Vickrey had invented something but it was not generally thought to be practical (although later it was discovered to have been actually implemented in stamp auctions in the 1870s - see Lucking-Reiley 2000). Others, notably Lloyd Shapley and Alvin Roth, had invented algorithms but some of the fundamentals had been discovered in parallel in the real world. The simultaneous ascending bid auction was an invention. It had not existed before. 

The broad proposal was to run all of the auctions for each packet of spectrum simultaneously. No bringing in each lots one at a time as might be done at an art auction. The auctions would occur and end at the same time. There would be multiple rounds of bidding, each with a start and end date. This was intentional to allow bidders the time to assess bids around them and adjust accordingly.

But there was an immediate problem: if you were a bidder, why would you want to ‘help’ your competitors in this way. Maybe it would be better to sit back and watch the show and swoop in at the end. And, of course, if everyone did this, then there would be no bids to examine. Information would not be revealed.

The solution that Paul and Bob came up with was someone inelegant to the formal theorist’s eye. But it was practical. They would explicitly push for activity. If you sit back and don’t bid, you can’t come back at a later stage. You have to be in it somewhere. The activity rules were someone complex and messy. To those of us who know Paul for beautiful expression, they were out of character. But they worked (Milgrom 2004). Without it, the auction could simply not have succeeded.

What the simultaneous ascending bid auction did was show economists the path forward to the design of markets. Hal Varian, Susan Athey and Preston McAfee took that lesson to ad markets at Google, Microsoft and Yahoo, and opened up the biggest and most intense auction markets ever. In each case, there was an inspiration coupled with theory-informed rules to make sure the sheep went in the right direction. What we saw was the invention of an economically significant industry. 

The prize

Paul’s doorbell rang again in October 2020. This time it was Bob Wilson at two’o’clock in the morning telling him that they had both just won the Nobel Prize. Paul seemed surprised. No one else was. Perhaps when he gave a Nobel lecture on behalf of Vickrey back in 1996, he hadn’t thought his work to have importance and had failed to cite it in that lecture. Vickrey would have.

But to many of us, Paul’s contribution to auction theory and the invention of new and novel auction formats, was part of his contribution. One could easily have imagined him sharing the prize with Hart and Holmstrom for contributions to contract theory. One could easily have imagined him winning the prize for work on information economics. When his students wrote about his contributions on his Wikipedia page, they wrote so much it stood (in 2014) as the longest Wikipedia entry for any economist. They wrote it to make it easier for the world to appreciate his contributions when the prize came. It was a sure thing investment.

References

Dasgupta, P, and J E Stiglitz (1988), "Potential competition, actual competition, and economic welfare", European Economic Review 32(2-3): 569-77.

Grossman, S J, and J E Stiglitz (1980), "On the impossibility of informationally efficient markets", American Economic Review 70(3): 393-408.

Lucking-Reiley, D (2000), “Vickrey Auctions in Practice: From Nineteenth-Century Philately to Twenty-First-Century E-Commerce", Journal of Economic Perspectives 14(3): 183-92.

McMillan, J (1994) "Selling spectrum rights", Journal of Economic Perspectives 8(3): 145-62.

Milgrom, P R (2004), Putting Auction Theory to Work, Cambridge University Press.

Milgrom, P R, and J Roberts (1982), "Limit pricing and entry under incomplete information: An equilibrium analysis", Econometrica: Journal of the Econometric Society 50(2): 443-59.

Milgrom, P R, and J Roberts (1986), "Relying on the information of interested parties", RAND Journal of Economics 17(1): 18-32.

Milgrom, P R, and R J Weber (1982), "A theory of auctions and competitive bidding." Econometrica: Journal of the Econometric Society 50(5): 1089-1122.

Myerson, R B, and M A Satterthwaite (1983), "Efficient mechanisms for bilateral trading." Journal of Economic Theory 29(2): 265-81.

Vickrey, W (1961), "Counterspeculation, auctions, and competitive sealed tenders", Journal of Finance 16(1): 8-37.

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Topics:  Industrial organisation

Tags:  Nobel Prize, auction theory, simultaneous ascending bid auction, spectrum auction

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