I'll post market design related news and items about repugnant markets. See also my Stanford profile. I have a general-interest book on market design: Who Gets What--and Why The subtitle is "The new economics of matchmaking and market design."
KENNETH ARROW’S LAST THEOREM by Paul Milgrom, in The Journal of Mechanism and Institution Design 9, no. 1 (2024): 7-11.
ABSTRACT: In Kenneth Arrow’s last week of life at age 95, he reported that “I began my research career with an impossibility theorem. If I had time now, my last theorem would be an impossibility theorem about social choice for environmental policy.” This paper completes the formalization, proof, and discussion of the theorem that Arrow then described.
Paul Milgrom forwards me this account of his testimony as an expert for the defense in the DOJ v Google trial on display ads. Expert testimony is partly theater, and parts of the article read like a theater review.
"Tuesday was dominated by the testimony of Google expert Dr. Paul Milgrom, Professor at Stanford University and the Chairman of “Auctionomics.”
"Dr. Milgrom is Google’s counterweight to the government’s Dr. Ravi.
"As soon as his testimony began, I realized he would be a formidable witness, not just because of his outstanding intellect and subject matter expertise, but because he is the kind of witness that is simply challenging for a counterparty to deal with. An older gentleman, he was equal parts charming, intelligent, poised, unflagging while enduring hours on the stand, and spoke with the quiet confidence and humility of the wisdom of his years.
...
"By presenting with charisma, charm, wit, and as one person described to me during a break, “grandpa vibes,” an outside observer who hails from most of the world’s cultures intrinsically wants to like Prof. Milgrom"
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Yesterday's post also touched on expert witnesses for the defense, from the DOJ's perspective:
Here's a press release from Auctionomics, the consulting firm run by Paul Milgrom and his business partner Silvia Console Battilana. They propose to repurpose water rights in a way that may resemble the recent incentive auctions for repurposing radio spectrum.
"Earlier this year, Paul co-hosted a conference at Stanford University attended by a group of economists, lawyers, and water experts. The group developed a proposal for a novel policy to fix the Colorado River crisis: the U.S. should redefine and buy back existing water rights,just as it did for misallocated rights to radio airwaves.
Auctionomics led the development of the FCC's Broadband Incentive Auction, converting TV licenses to new valuable uses. The current issues with water rights are similar to those of the radio spectrum, where existing rights holders with solid legal standing were hesitant to change the status quo, despite the clear misallocation of resources.
However, Auctionomics successfully addressed the problem with its innovative auction design, facilitating next-generation telecommunications and raising $19.8 billion while safeguarding existing broadcasters.
The Colorado River proposal aims to address deficiencies in the current water rights allocation system. The existing system hinders mutually beneficial trades between users and prohibits water banking - a means to enable farmers or cities manage current water use more efficiently, leaving more in reservoirs for future dry periods.
While there are historical reasons for these limitations - the uses of river water are diverse, interconnected, and poorly measured. Modifying them can result in severe consequences in a system that guarantees inefficiency and overconsumption. However, the same model employed to redistribute broadband spectrum can incentivize water rights holders to use their water more efficiently.
Auctionomics aims to adapt this model to the Colorado River with practical steps involving a hydrological survey, voluntary redefinition of water rights, and purchasing enough new rights from willing sellers to meet the necessary reductions in total consumption."
"“People get confused when they think about auctions, they think about bidding for a piece of art or something like that,” Milgrom told ZME Science in an interview. “What economists mean when we talk about auction is a process of decentralized resource allocation using prices. It means that we’ve got people who have knowledge about what they need and how valuable things are to them, and we take account of that information to allocate resources specifically, we make bids, and those things are converted to determine prices.”
“If you’re not using an auction you either mean you’re not using prices to guide the resource allocation or you’re not using individual bids. If you don’t use that information, you’re gonna have waste.”
"Waste also means opportunity, and the opportunity Milgrom sees would be transferring water use from those who value it less to those who value it more (and are willing to pay more for it).
...
“In California, less than 5% of water is reallocated, even in the most severe drought,” Milgrom says
“The prices adjust [water gets more expensive], but the reallocation doesn’t adjust even when there is insufficient water. The prices are responsive, but the value of trade isn’t very responsive. So why doesn’t the market work, and what can we do to fix it?”
“It’s not what you expect in a market. What you would expect in a well-functioning market is that the water allocation would increase more to adapt to sending more water into higher value uses and less water into less-value uses. So we’d expect more trading to go on. The fact that it didn’t suggests there’s a problem with the market.”
...
"Designing a large-scale market for water isn’t without precedent. In Australia, a much larger proportion of water is being traded (about 50%); with a roughly similar standard of living, and similar environmental challenges, people in Sydney use about half that amount. But while Australia can serve as an inspiration for California, the same system can’t be replicated exactly.
“We can’t apply the Australian model to California because there are different property rights regimes, the rights are defined differently. They also don’t take into account return flows, which California water law does.”
...
"“I’m cautiously optimistic,” Milgrom says, drawing from his experience with auctioning broadcast spectrum space. “Part of what’s making me optimistic that this is the right time is the progress in measurements and hydrological models.”
The video is at the link, there are four ten minute discussions, followed by brief responses by Paul and Bob.
My discussion of Bob Wilson begins at around 27:20, and my final words to him were "Bob: you saw and demonstrated the future of game theory in economics, earlier and more clearly than anyone else. We’re all lucky to know you."
AEA Nobel Laureate Address Honoring the 2020 Nobel Laureates Paul R. Milgrom (Stanford University) and Robert B. Wilson (Stanford University) January 8, 2022 at 2:30 PM ET View Recording
Presiding:Christina D. Romer,University of California-Berkeley
G translate: Paul Milgrom and Robert Wilson. From theory to practice in auctions
Here's one snippet:
"R. Wilson ([1967], [1969] and [1977]) provided the first analysis of Bayesian equilibrium strategies in the case of a common and uncertain value. This work was extended by P. Milgrom [1981a] and by many other authors subsequently. [6] Introducing the hypothesis of conditional independence according to which the signals received are positively correlated, Wilson [1969] thus showed that, in this context, the winner was the one who overestimated the true value of the object the most. He also highlighted how agents should determine their offers by incorporating into their strategies that the winner is the one with the highest signal."
"In 1991 Alvin Roth, who in 2012 would share the Nobel prize for economics, was asked how the discipline might change over the century to come. “In the long term”, he wrote, “the real test of our success will be not merely how well we understand the general principles which govern economic interactions, but how well we can bring this knowledge to bear on practical questions of microeconomic engineering.” Sweden’s Royal Academy of Science seems to agree. On October 12th it gave this year’s Nobel prize to Paul Milgrom and Robert Wilson, both of Stanford University, for their work on auction theory and design. Their work epitomises economics as engineering.
...
"The pursuit of economics as a form of engineering means that Messrs Milgrom and Wilson are more enmeshed in the real world than the typical academic. Both have consulted for regulators and firms. Mr Milgrom advised Time Warner and Comcast on their participation in radio-spectrum auctions in 2006; his efforts helped save his clients more than $1bn. In 2009 he co-founded a firm, Auctionomics, that provides consulting services to those looking to operate and to bid in auctions (many of the sort designed by the prizewinners).
"It is a different sort of work from that which many aspiring scholars imagine themselves to be pursuing. But the rewards the laureates have reaped in academia and beyond certainly advertise the power wielded by economic engineers."
Paul Milgrom and his business partner Silvia Console Battilana describe how market design can reallocate scarce resources from spectrum licenses to water rights.
"Misallocation of scarce resources too often deprives users of them even as others waste their supply. Well-designed markets can overcome such problems by enabling voluntary transactions that allow existing users to retain their allotments while enabling higher-value uses.
...
"Many of the world’s existing rights to fresh water – both surface water and groundwater – have already been granted and grandfathered in complex ways to cities, farmers, and industrial users. In some cases, each individual trade of these rights requires governmental approval; other jurisdictions prohibit such trading entirely.
"These restrictions and historical rules have led to highly inefficient allocations. Water may be unavailable to towns that require more of it as they grow, even when those urban and residential uses are a hundred times more valuable than the rural ones they would supplant. Certain industrial firms whose rights are based on historical use may have an incentive to overuse water, even during droughts, to retain their rights to future allotments. Where trading of rights is limited or prohibited, poor price signals make it difficult even to assess which uses are most valuable. And water demand will increase and shift as climate change continues to upend historical usage patterns.
"The success of the US radio spectrum auction points to a solution. Instead of revoking incumbents’ spectrum rights unilaterally, Congress redefined them in a way that made trading them possible and simple, and then allowed TV broadcasters to decide for themselves whether to continue their previous uses or decline to participate. The rights that were sold were then reconfigured to be suitable for new uses and efficient trading, while those that were unsold remained fit for existing purposes."
American Economic Review 2021, 111(5): 1383–1405 https://doi.org/10.1257/aer.111.5.1383
Here are a few of the introductory paragraphs:
"Game-theoretic modeling of auctions began in the 1960s with a pair of seminal papers by William Vickrey (1961, 1962) and the brilliant but unpublished doctoral dissertation of Armando Ortega-Reichert (1968). Robert Wilson (1977, 1979) became the next important contributor to auction theory research and, as Wilson’s student, I was inspired to make auctions and bidding the subject of my doctoral dissertation.
...
"Most of my work published in academic journals is theoretical, proving theorems about the properties of abstract models, but developing and participating in real-world mechanisms requires more than that. Two important lessons that I learned from working on high-stakes auctions are that they operate in an almost infinite variety of contexts, and that this variety is the reason for the paradoxical importance of including unrealistic assumptions in models built to understand and illuminate reality. No single set of assumptions is adequate to describe all the various settings in which auctions are used, and too much specificity in models can blind the analyst to important general insights.
...
"Why do economists rely on such unrealistic assumptions? It is because a well-chosen simplification can remove the dust and smoke that obscures our view of the workings of economic forces. Although we celebrate the resulting theorems for the insights they deliver, we can apply them successfully only by being vigilant, working hard to understand not just the insights that simplified analyses provide but also how the designs and rule choices they inspire must be adapted to withstand the dust and smoke and also the much larger disturbances of the particular worlds in which the mechanisms will operate."
And here are the concluding paragraphs:
"Auction theory has changed substantially since I made my first studies in what were still its early days. Although the “unrealistic” models of those times have proved their worth in guiding practical auction designs, some of that guidance was off point. In my own work, this showed up in the traditional analysis of the exposure problem. Despite the theoretical worst-case conclusion that exposure problems are intractable, we found that they could sometimes be quite manageable in practice.
"For the future, simulations and computational methods are likely to be increasingly important. Yet, it still takes theory to understand problems and the scope of proposed solutions. The time has come for old methods and new to work hand in hand."
Here's a celebratory account of the Nobel winning work of Milgrom and Wilson. The authors have used the new AEA symbol for random ordering of authors, which I can't reproduce here (it's an r in a circle..)
by (in random order) Alexander Teytelboym Shengwu Li Scott Duke Kominers Mohammad Akbarpour Piotr Dworczak, March 13, 2021
Abstract: The 2020 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel was awarded to Paul R. Milgrom and Robert B. Wilson for “improvements to auction theory and inventions of new auction formats.” In this survey article, we review the contributions of the laureates, emphasizing the subtle interplay between deep theoretical questions and practical design challenges that resulted in one of the most successful fields of economics.
Columbia University Press posts a "video of Paul Milgrom's 2014 Kenneth J. Arrow Lecture that inspired Discovering Prices: Auction Design in Markets with Complex Constraints. Paul Milgrom discusses how prices can guide decentralized resource allocations in environments with non-convexities. His work on auctions led the Royal Swedish Academy of Sciences to award him and Robert Wilson the Nobel Memorial Prize in Economic Sciences for improvement to auction theory and invention of new auction formats."
This was a Nobel year unlike any in recent memory, since the Covid pandemic prevented the festivities from being held in Stockholm as they usually are. The Nobel lectures by Milgrom and Wilson were recorded at Stanford, and they received their medals from the Swedish consul in a private ceremony.
"It was the first to be awarded outdoors and the first outside of Stockholm.
It was the first economics prize awarded to a student (Paul) with his disseration adviser (Bob).
It was the first awarded jointly to two people living across the street from one another.
Paul became the first to give TWO Nobel prize lectures, having already lectured on behalf of Vickrey in 1996.
The backyard ceremony was held behind a residence that had housed two economics laureates (Paul Milgrom & Joe Stiglitz), plus 3-time SuperBowl winning coach Bill Walsh!
"Also unusual is that, by focusing on Paul's auction contributions, the Nobel Committee had left unmentioned ten of Paul's twelve most highly cited publications."
"there are many cases where the “invisible hand” does not work. Prof. Wilson’s analysis of the winner’s curse in common-value auctions is a prominent example. “Sometimes the invisible hand needs a bit of help, and that’s where market design comes in – for instance, making sure bidders can update their value estimates during the bidding process itself”
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Here (live streamed today on Dec. 16) is an event originating in Vienna, including a video interview in which I talk to Ben Greiner. (It starts at 6pm CET, i.e. 9am PST):
"This event is being organized by the WU Department of Economics
"Nobel Prizes are awarded every year in December, on the anniversary of Alfred Nobel’s death. Nobel laureates are celebrated in the media, but hardly anyone knows anything about the research that goes on behind the scenes. We plan to change that. In cooperation with experts, we will be introducing the work of the winners of this year’s Nobel Prize in Economic Sciences in terms that even laypeople can understand. We will analyze the innovative power of the work and discuss its significance and potential applications in practice.
Welcoming words: Tatjana Oppitz, Vice-Rector for Infrastructure and Digitalization
Discussion: Maarten Janssen, Professor of Economics, University of Vienna
Maarten Janssen is Professor of Microeconomics at the University of Vienna. Among many others, his research interests are in the fields of game theory, industrial organization and competition policy, and in particular auctions. He is particularly interested in the implications of information asymmetries in markets and market design.
Stefan Felder, Rundfunk und Telekom Regulierungs-GmbH: RTR
Stefan Felder studied at Technical University and University of Economics and Business in Vienna. He worked in the telecommunications industry and at the University of Vienna. As of 1998, he has been a member of the Austrian Regulatory Authority for Broadcasting and Telecommunications (RTR). He is an expert on spectrum auctions, competition analysis, and mobile communications. He is Head of Spectrum and Mobile Market at RTR.
Moderation: Maria Marchenko, WU
Maria Marchenko is an Assistant Professor at the WU Department of Economics. Her research lies in the fields of applied and theoretical econometrics using state-of the art techniques and theoretical concepts with applications to networks and labor market.
Video interview: Alvin E. Roth, Winner of the Nobel Prize 2012; Professor of Economics, Stanford University
Alvin E. Roth is Professor of Economics at Stanford University. In 2012, he won the Nobel Prize in Economic jointly with Lloyd Shapley “for the theory of stable allocations and the practice of market design.’’
by Scott Duke Kominers and Alexander Teytelboym, JOURNAL OF ECONOMIC LITERATURE, VOL. 58, NO. 4, DECEMBER 2020, (pp. 1180-96)
Abstract: Designing marketplaces in complex settings requires both novel economic theory and real-world engineering, often drawing upon ideas from fields such as computer science and operations research. In Discovering Prices: Auction Design in Markets with Complex Constraints, Milgrom (2017) explains the theory and design of the United States' "incentive auction" that reallocated wireless spectrum licenses from television broadcasters to telecoms. Milgrom's account teaches us how economic designers can grapple with complexity both in theory and in practice. Along the way, we come to understand several different types of complexity that can arise in marketplace design."
And from the conclusion:
"So what have we discovered from Prices? Modern marketplace design increasingly wrestles with complexity; as it does so, we need novel, tailor-made theory as well as supporting infrastructure. Complexity has real economic meaning—and can take multiple forms."
"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."
"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."
In my limited experience (but not just limited to my own experience) Nobel prizewinners are often asked about how they were notified of the fact that they won the prize, and by whom. Paul Milgrom and Bob Wilson certainly have one of the best stories to answer that question, and millions of people have already viewed the video from the Milgroms' Nest doorbell camera, as Bob tried to arouse Paul and give him the news.
The Nest doorbell broadcast also to Paul's wife Eva, who was visiting family in Stockholm, and who was alerted at the same time he was. Here's the view from the Swedish press (including a video of the video playing on her laptop...):
"AS: We just spoke with Paul Milgrom and he said that he heard the news by you walking across the street and ringing his doorbell.
RW: Well that’s right because he had turned his phone off for the … to get a good night’s sleep, and so somebody had to wake him, and he lives across the street so I just walked over and knocked on the door. I roused him.
AS: I think … I think this must be a first in the history of the Nobel Prize.
RW: Yes, how many times does … first to have a knock on the door, which sounds like something from the 19th century, and secondly that in fact the two of us live only, what, 40 m apart."
*****************
It turns out that Bob Wilson went to Lincoln High School in Nebraska (and that you can never escape your high school):
"The Lincoln High School wall of distinguished alumni — the one with photos lining the school's main hallway — will need to make room for another photo.
"Robert Wilson, who graduated from Lincoln High in 1955, left for Harvard on a prestigious scholarship and ultimately landed at Stanford, won the Nobel Prize in economics Monday."
The day of the prize, the NY Times story by Jeanna Smialek got this fairly coherent quote from me before dawn:
“They haven’t just profoundly changed the way we understand auctions — they have changed how things are auctioned,” said Alvin E. Roth, a Nobel laureate himself who was one of Mr. Wilson’s doctoral students.
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Joshua Gans, one of Paul's students, republished the remarks he had made on the occasion of Paul's 65th birthday (long ago...)
"There are so many things one could say about Paul but it turned out that I said what I wanted to say back in 2013 at a conference in his honor to celebrate his 65th Birthday."
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Bob's longtime colleague (and my one time housemate when we were grad students) David Kreps has a lovely essay, which includes this quote from Hugo Sonnenschein:
"Great economists write great papers. But the greatest economists are those who found new schools of thought."
"impact on the discipline of economics, in my opinion, puts him in the company of giants such asKen ArrowandPaul Samuelson: Bob is, as much as anyone, the founder of the “School of Economic Theory as Engineering.” Both in his own work, but even more through his influence on his students and colleagues, Bob has brought economic theory to the real world, both as a mechanism for understanding “how things work” and then in the design of better institutions. The Nobel Prize announced today is for his and Paul’s work on the design of complex auctions, such as the spectrum auctions, which is a prime example of economic theory as engineering. But, in addition:
Bob himself has taken the theory of nonlinear pricing to practical applications in electricity markets.
His student, Nobel Laureate Al Roth, brought matching-markets theory to the design of assignment algorithms, assigning MDs to internships, and to kidney exchange “markets.”
His student, Nobel Laureate Bengt Holmstrom, brought incentive theory to practical considerations in the design of pay-for-performance systems (some in collaboration with Milgrom) and, more recently, to issues in financial institutions.
His student and co-Nobel Laureate Paul Milgrom, besides his work on auction design, and in collaboration with our colleague John Roberts, brought economic theory to bear on the design and management of complex organizations (which, for my money, is even more important than his pathbreaking work on auctions; Paul could have been given the Nobel for any of several different topics, and his work on “the modern corporation” happens to be my personal favorite).
And it continues: A third generation — students of Paul, Bengt, and Al, as well as others who have embraced this style of work and so became “adopted” members of Bob’s tribe — are building an intellectual edifice that mixes superb theory with real-world insight and applicability."
***************
Did you know that Paul has a company? Here's the tribute on the Auctionomics website:
Could this be the best Nobel pairing ever? (It's certainly a great one, and one of the best things to come out of 2020 so far...) Here's the announcement:
"The 2020 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel has been awarded to Paul R. Milgrom and Robert B. Wilson “for improvements to auction theory and inventions of new auction formats" https://www.nobelprize.org/
I've known Paul at least since 1978, when he attended a course I taught while on leave at Stanford, on Axiomatic Models of Bargaining. Bob advised both of our dissertations, although not at the same time.
Bob is a legendary advisor of grad students. Paul is now the third of Bob's students to win a Nobel. So Bob is well established as the patriarch of a Nobel dynasty.
Bob Wilson's Nobel dynasty (to date): Wilson (with Milgrom) 2020, and Bob's students Roth (with Shapley) 2012, Holmstrom (with Hart) 2016, and Milgrom (with Wilson) 2020
It looks like we should check back in 2024...
Here's another picture, from another celebration:
Bob Wilson being celebrated for the 2017 CME MSRI prize, by his students Al Roth, Paul Milgrom, and Bengt Holmstrom.
I've often blogged about both Milgrom and Wilson, separately and together.
Here's a paragraph I wrote about Bob's work in our (only) joint paper, in which we interviewed each other:
Alvin E. Roth and Robert B. Wilson Journal of Economic Perspectives—Volume 33, Number 3—Summer 2019—Pages 118–143
"Wilson (1977) introduced the model of common-value auctions (sometimes called the “mineral rights model”). The model and its equilibrium initiated a large body of theoretical, experimental, and applied work. One important insight from this model is that winning an auction contains “bad” news, since it implies in equilibrium that the winner’s estimate is the highest. In equilibrium, rational bidders fully account for this, but the paper raises the empirical question of the extent to which actual bidders are able to fully discount for the fact that, if they win the auction, they likely overestimated the value of winning. Thus, Wilson’s work initiated a new research program on the winner’s curse, involving systematic overbidding compared to equilibrium, sometimes involving losses to the winning bidder. The private-value model of Vickrey (1961) and the common-value model of Wilson (1977) together form the basis of much of modern auction theory and practice, since most auctions
have elements of both private and common value."
Right after that, Bob and I talked about important influences on our work. Bob included this:
"I was deeply affected in the early 1990s by working with Paul Milgrom on design of the FCC spectrum auctions. I marveled at his insights and creativity in constructing rules for a “simultaneous ascending auction” that would have good prospects of yielding an approximately efficient outcome in an environment afflicted with strong complementarities, dispersed private information about market fundamentals, and substantial market power."
To which I replied:
" I was also much influenced by Paul when we developed and co-taught what may have been the first courses in market design, in 2000 and again in 2001 when he was on leave at Harvard and MIT."
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Here's an old snapshot:
Bob Wilson and Paul Milgrom in 2006
There's a rabbinical literature about the relationships between students and teachers. It often comes to mind when I think about how lucky I have been to have the students I've had. But today I'm reminded of my luck in having Bob Wilson as my teacher and friend, and Paul as my friend and colleague.
"Joshua ben Perahiah used to say: provide yourself a teacher and acquire yourself a friend. Judge everyone favorably." (Pirkei Avot, chapt 1 verse 6)
Here's how I recalled Bob as a teacher, in an autobiographical essay of a kind that they will each now be asked to write:
"Bob Wilson agreed to be my advisor and rescued me from having what looked to be a very short academic career after I failed one of my Ph.D. qualifying exams. He was on sabbatical that year, but met with me regularly once a week for an hour. In memory, our meetings followed a kind of script: I would spend a while explaining to him why I hadn’t made progress that week, and then he would spend a while telling me not to be discouraged. Then I would describe some roadblock to further progress, and he would, as we finished our meeting, recommend a paper for me to read. Because his recommendations had always been very much on target, I would go straight from his office to the library and start to read the paper. As I did, I would think, this time Bob made a mistake, this paper has nothing to do with my problem. But then, somewhere in the middle of the paper would be a lemma or remark that helped me get around that roadblock …"
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And here's a final picture from Stockholm in 2012, of me and Emilie and Paul and Eva, with Parag Pathak (one of Bob's academic grandchildren) in the background.
“for improvements to auction theory and inventions of new auction formats”
...
“This year’s Laureates in Economic Sciences started out with fundamental theory and later used their results in practical applications, which have spread globally. Their discoveries are of great benefit to society,” says Peter Fredriksson, chair of the Prize Committee." Learn more in the popular information
"Every day, auctions distribute astronomical values between buyers and sellers. This year’s Laureates, Paul Milgrom and Robert Wilson, have improved auction theory and invented new auction formats, benefitting sellers, buyers and taxpayers around the world." Read the scientific background
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