Friday, May 6, 2011

Milgrom on market design

Paul Milgrom has an article in the latest  (April 2011) issue of Economic Inquiry:
CRITICAL ISSUES IN THE PRACTICE OF MARKET DESIGN

Abstract: The years since 1994 have witnessed the emergence of market design as a new discipline within economics, in which research and practice exert powerful mutual influences in matching and auction markets. The problem of designing well-functioning auction markets has led economic designers to revisit such fundamental issues as the definitions of commodities, the ways participants communicate with markets, the trade-offs between the incentives provided for truthful reporting and other attributes of mechanism performance, and the determinants of the scope of markets, especially whether and how trade in different goods is linked.

Thursday, May 5, 2011

Nonsimultaneous kidney exchange chains produce more transplants than simultaneous chains (published)

When I published the earlier post with the same name, the paper hadn't yet been published, and medical journal rules meant that I could only link to an abstract.

Now the paper has appeared, and you can read it here:

Ashlagi, Itai, Duncan S. Gilchrist, Alvin E. Roth, and Michael A. Rees, ; ''Nonsimultaneous Chains and Dominos in Kidney Paired Donation -- Revisited,'' American Journal of Transplantation, 11, 5, May 2011, 984-994. 

Wednesday, May 4, 2011

Misc. kidney exchange

A larger than usual exchange in SF: SF hospital performs 10-person kidney exchange
"Five people have received healthy kidneys from five donors in what may be among the largest kidney exchanges at a single hospital in California.

"The swap at California Pacific Medical Center took place on Friday during a series of operations, the San Francisco Chronicle reports.

"This has been bread-and-butter for us for a few years; we've just never done one of this size," said Dr. Steve Katznelson, medical director of California Pacific's kidney transplant program. "There are all sorts of logistics involved, and it's hard to do."
******

Kidney exchange in India is still rare (but not rare like a unicorn): Two women in kidney swap to save life of other’s spouse
"Dr H Sudarshan Ballal, medical director and chairman, medical advisory board of Manipal Health Enterprises, said swap transplants are common in the US but not so in India. "One of my earlier patient was a middle-aged woman whose husband was a potential donor but incompatible with her. They migrated to the US and later told me they had done a swap with a Jewish couple there. We've been trying for a long time to make swap transplants happen but managed it this time," he said. "

****
Here's an account of a non-simultaneous nondirected donor chain at St. Barnabas hospital in New Jersey, conducted around Valentine's day, with reporting of an April 2011 meeting of patients and donors: Donors, recipients in chain of eight kidney transplants gather for reunion.
The non-directed donor chose to remain anonymous "I’ve got some new scars, but that’s it," the donor said. "I’d rather it not be a big deal."

Tuesday, May 3, 2011

Bait and switch in law school admissions?

A much blogged about article in the NY Times discusses how law schools offer many admitted students merit scholarships whose continuation depends on their maintaining a certain grade point average. The article notes that, coupled with forced-curve grading policies, this sometimes means that many of those with first year scholarships will inevitably fail to maintain their eligibility for continued scholarship assistance. It argues that the algorithm used by US News and World Report to rank law schools plays a role, by focusing on statistics for the entering class.

Law Students Lose the Grant Game as Schools Win

"Why would a school offer more scholarships than it planned to renew?


"The short answer is this: to build the best class that money can buy, and with it, prestige. But these grant programs often succeed at the expense of students, who in many cases figure out the perils of the merit scholarship game far too late.

"On the Golden Gate campus recently, a group of first-year students at risk of losing their scholarships were trying to make sense of the system. Most declined to be identified for this article because criticizing the school seemed, at minimum, undiplomatic. But the phrase “bait and switch” came up a lot. Several assumed that they were given what is essentially a discount to get them in the door.
...
"If it sounds absurd that America’s legal education system could be whipsawed by, of all things, U.S. News, you have yet to grasp the law school fixation with rankings. Unlike undergraduate colleges, law schools share far more similarities than differences, particularly in the first-year curriculum.


"So a lot of schools regard the rankings as their best chance to establish a place in the educational hierarchy, which has implications for the quality of students that apply, the caliber of law firms that come to recruit, and more. Striving for a high U.S. News ranking consumes the bulk of the marketing budget of a vast number of schools.

"Which is where scholarships come in.

"The algorithm used by U.S. News puts a heavy emphasis on college grade-point averages and Law School Admission Test scores. Together, those two numbers determine about 22 percent of a school’s ranking. The bar passage rate, which correlates strongly with undergraduate G.P.A.’s and LSAT scores, is worth an additional two points in the algorithm. In short, students’ academic credentials determine close to a quarter of a school’s rank — the largest factor that schools can directly control. "

Monday, May 2, 2011

Love and Warcraft

Any venue in which lots of single people invest time and energy in something that interests them can provide the thickness needed for an effective mating market.  You can get a date by being an active Yelp reviewer*, and, it turns out,  World of Warcraft isn't bad either, as Stephanie Rosenbloom reports in the NY Times: It’s Love at First Kill

" With more than 12 million subscribers, World of Warcraft is one of the most popular games of its kind in the world (others include EverQuest, Aion, Guild Wars). That’s a sizable dating pool. Match.com, by way of comparison, has fewer than 2 million subscribers."


***
*My new HBS colleague Mike Luca has studied Yelp, including (in passing) the way that they create a social network for their most active reviewers.

Sunday, May 1, 2011

“Matching markets: Theory and practice”

That's the title of this paper by Atila Abdulkadiroglu and Tayfun Sonmez, presented at the 2010 Econometric Society World Congress, in Shanghai.

Yeon-Koo Che has just posted his discussion of that paper. Among other things, he suggests that one reason we don’t see more centralized clearinghouses is that they don’t necessarily create Pareto improvements, and a hybrid approach is worth thinking about. (For example, he speculates, maybe a centralized clearinghouse for college admissions could be started if it explicitly allowed colleges to continue to engage in early admissions, and only tried to organize the "regular admissions" part of the market.)

Saturday, April 30, 2011

Designing "hidden markets"--Sven Seuken

Yesterday Sven Seuken defended his dissertation, which is on the interface of CS and Economics. In particular, he is interested in designing both computerized marketplaces and the user interfaces through which participants will interact.



The essay that was his job market paper concerns a practical business idea for a centrally administered marketplace for peer-to-peer computer backup services that have to be consumed in bundles (e.g. bandwidth and memory are complements), but may be offered in different proportions by different users, at market prices that are posted through a user interface that makes it easy for a consumer to see what backup he requires, and what combinations of resources he can offer to the system to pay for his own services. A customer for the backup service must offer backup services to other customers, and the  centralized server keeps track of what resources are being used, and sets relative prices for different resources that are “hidden” in that they are revealed not as numerical prices, but as tradeoffs between backup capacity a consumer demands and various ways that he can supply the system with resources from his own computer (upload and download bandwidth and memory, and hours a day connected to the web).

That is, this is a market with complements, in which both bids and asks must be for packages of services, but in which customers can participate using a simple interface.

Market design itself is becoming a market with complementarities between economists and computer scientists. Sven may join his main advisor, David Parkes, in internalizing many of these complementarities himself. (The other members of his committee were Eric Horvitz, Yiling Chen, and me.) Since he is going to Zurich, he may also have the opportunity to join forces with Jacob Goeree and solidify a real center of market design there.


Welcome to the club, Sven.

Friday, April 29, 2011

First kidney exchange in Spain

La Vanguardia reported yesterday on a nondirected donor chain, the first in Spain (and I think the first kidney exchange in Spain):

Éxito en la primera cadena de trasplante renal de vivo con 'buen samaritano'
El primer 'buen samaritano' de España es un religioso de Barcelona que de forma altruista y anónima ha entregado uno de sus riñones a un desconocido, logrando que se beneficiaran tres personas

The first 'Good Samaritan' non-directed donor in Spain is a priest from Barcelona who initiated a chain of three transplants.

And here's the article from El Pais:
España realiza el primer trasplante de vivo en cadena gracias a un donante altruista
Tres pacientes se han podido beneficiar del procedimiento.- Con este sistema, la ONT espera mantener la elevada tasa de trasplantes de España

See my earlier post about Mike Rees and Spain:

"Una persona altruista puede salvar muchas vidas"

"A selfless person can save many lives"

HT: Rosemarie Nagel and 'Chris F. Masse'

Thursday, April 28, 2011

Expectations and reference points: Andreas Fuster

Andreas Fuster successfully defended his dissertation today on various aspects of behavioral economics. The part that was his job talk was his experimental paper, “Expectations as Endowments: Evidence on Reference-Dependent Preferences from Exchange and Valuation Experiments,” written with his fellow graduate student Keith Ericson and forthcoming in the QJE. The high level motivation for the paper is to study carefully in the lab how expectations are important for consumer decisions, and to better understand how expectations are formed. The more particular focus of the paper is reference-dependent preferences, with the idea that reference points are determined by expectations as formulated by Koszegi and Rabin. And the very particular focus of the paper is the recently controversial “endowment effect,” related to experimental observations that subjects seem reluctant to trade objects with which they are endowed.



Andreas and Keith explore whether the “reference point” that subjects form is related more to their expectations about what they may own in the future than to their current endowment. In a very carefully designed experiment, they manipulate expectations by assigning subjects a probability that they will receive an object, or have an opportunity to trade it, and then observe various measures of how subjects evaluate the object as a function of these probabilities.  Their results provide the most convincing support to date of the Koszegi-Rabin model of expectation based reference points.


When asked how he planned to spend the rest of the day, Andreas replied "PhD: pretty heavy drinking."

Welcome to the club, Andreas.

Deceased donor kidney allocation--webinar today

The UNOS Kidney Transplantation Committee proposal to change the existing kidney-allocation policy for deceased donors
Webinar: Thursday, April 28, 2011
Eastern time: 3:30 - 5:00 p.m. Central time: 2:30 - 4:00 p.m.
Mountain time: 1:30 - 3:00 p.m. Pacific time: 12:30 - 2:00 p.m.

 

Speakers/Faculty:
Kenneth Andreoni, MD, Chair, United Network for Organ Sharing Kidney Transplantation Committee; Associate Professor of Surgery, Ohio State University, Columbus, OH
Benjamin Hippen, MD, Metrolina Nephrology Associates, P.A. and the Carolinas Medical Center, Charlotte, NC
Dorry Segev, MD, Associate Professor of Surgery and Epidemiology, Director of Clinical Research, Division of Transplantation, Johns Hopkins Medical Institution, Baltimore, MD
Tom Mone, CEO/Executive Vice President, OneLegacy Organ Procurement Organization, Los Angeles, CA
Supplemental Materials:

Jim Warren, Editor &; Publisher, Transplant News - Moderator 


*********
See my earlier posts on this proposed policy change in the allocation of deceased donor kidneys:

Wednesday, April 27, 2011

The underlying structure of matching models: Scott Kominers

Scott recently finished his unusually well attended dissertation defense. He's engaged in a wide ranging effort to prove all the familiar theorems about matching models without any of the familiar assumptions, or at least with a demonstrably minimal set of assumptions, and hence to discover why things work in models of who gets what.

John Hatfield, on the right in the picture below, is one of Scott's chief co-conspirators.


And here they are, getting down to serious drinking afterwards:
(QED:)


Welcome to the club, Scott.

Tuesday, April 26, 2011

A match for the law firm market?

Paul Kominers points me to this item: New ‘JD Match’ to Help Law Firms Find Law Students to Interview; K&L Gates Giving Service a Tryout

"Tired of the traditional on-campus law school interviewing process? A consultant may have the answer for some who would like to deal more directly with law firms and other legal employers seeking law students who want to apply for work.

 And here's a longer article from the Am Law Daily, which suggests that unraveling is the motivator, and a deferred acceptance algorithm is part of the proposed solution: JD Match Aims to Fix the Law Firm Recruiting Process

"On Monday, Ashby Jones at The Wall Street Journal's Law Blog lifted the curtain on JD Match, a new product that will try to connect job-seeking law students with firms. For a $99 fee, students upload their resume and basic information to JD Match, then rank the law firms where they’d like to work. The law firms, in turn, rank students. An algorithm matches firms and students based on their rankings.


"It seems like such a nifty, logical concept that we at The Am Law Daily are kicking ourselves for not thinking of it first. We reached out to the driver behind JD Match, law firm consultant and Adam Smith, Esq. blogger Bruce MacEwen, to find out more. Following is an edited transcript of our phone conversation on Tuesday.

What was the genesis of JD Match?

"People have been kicking around the idea about doing something about the dysfunctional law firm recruiting model for a long time. [Harvard Law School professor] Ashish Nanda wrote a piece in The American Lawyer last January addressing this very thing.... And from my perspective, the great train wreck of the 2008/2009 recession really revealed the flaws in the system.

There's this arms race to interview earlier and earlier. It's not a smoothly functioning market at all. The economist in me just found that infuriating. So my partner Janet Stanton and I started talking about doing something like this, probably shortly after Ashish's article came out.

We did an extensive amount of research with managing partners at firms, hiring partners, career services people at law schools, and even students and junior associates, and quickly realized that the medical matching model which Ashish had written about was not going to work in our world. To begin with you can't make anything mandatory with law firms. Nevertheless, we were inspired by the idea of having an algorithm at the heart of the process.


How will the algorithm work?

"The algorithm will run three times in the OCI recruiting season: August, September, and October. What it does is assume the Econ 101 truth that each firm and each student is in the best position to determine what's in their self-interest. So the only input to the algorithm is preferences for firms for students and preferences for students for firms. That's it. No qualitative or quantitative information whatsoever.

"The assumption is that the preferences represent all the distilled information--research, anecdotes, gossip, whatever--that firms have about students and students have about firms. When the algorithm runs, a couple of things happen. First, no student and firm wlll ever be paired unless it's mutual. So if I didn't put Skadden on my list, it doesn't matter if Skadden loves me. I'm not going to be matched with Skadden.


So give me a hypothetical scenario of how this would work.

"Let's pretend I did put Skadden as my first choice and they did have 25 spots. I will tentatively, as the algorithm is running, be matched with Skadden unless and until I get bumped because Skadden gets matched with 25 students it likes more than it likes me. And then I go to my next available firm that has a seat for me. And then it goes on like that.

"Students get [matched with] one and only one firm on the theory that they can only take one job. Firms will get as many students as they said they have slots or maybe fewer if not that many students like them. But they won't get more. So this helps firms manage yield. And two professors of law [Kevin Quinn at the University of California at Berkeley and Andrew Martin at Washington University in St. Louis] are writing the algorithm for us.

Why will you run the algorithm three times?

"Let's pretend that I'm a law student back at Stanford but I have delusions about what a hot commodity I am. Let's say the first 15 firms I rank are highly aspirational: Skadden, Davis Polk, Cleary. You know. The usual suspects. So the August match runs, and I find out that I was matched with firm number 17. Well, this is a reality check for me. It's unfiltered, real-time market information and that should tell me for the September match and OCI, I need to be a little more realistic.

Is there a baseline number of students and firms that JD Match will need to sign up in order for the process to work efficiently?

"Yes. We have four Am Law 30 firms signed up including K&L Gates. We can't name the other three yet, but they will come out shortly. We've been previewing JD Match primarily to the law firms, but we've also reached out to the law schools. The schools are intrigued. They're a little nervous about upsetting the OCI process that they drive, but they do understand JD Match provides an overlay to the process as it currently works. We don't change anything about OCI.

What else do you have in the works?

"We are creating something called the JD Match Institute which we will fund out of our revenues. And its designed to begin to look at the data we will be gathering and suss out what actually makes for successful lawyers.

"Our strong suspicion--confirmed by [University of Indiana professor] Bill Henderson--is it ain't GPA. In version 2.0 of JD Match we will introduce some psychographic and behavioral testing for students. Voluntary, obviously, but there are very few law firms that are doing this. McKenna Long is doing it. Some firms like K&L are doing it in the U.K....

"What we think we can develop in fairly short order is empirical evidence of what makes for a successful lawyer and that would be tremendously exciting for us because law firms could begin to hire a little more rationally. Frankly I think it could only be good for the students. There are 40,000 law students in the U.S. and how many of them are on the Harvard Law Review? But a lot of them could be great with clients, could be responsive, could be team players, could be emotionally intelligent....It could only open up more doors."

Monday, April 25, 2011

Pre-kindergarten and school choice in Boston

Boston has a pre-kindergarten program that doesn't have enough spaces to meet demand, particularly because it is an entryway into the full public school choice process: a child who gets a good school for pre-K is guaranteed to be able to stay there for elementary school.

Stephanie Ebbert picks up the story in the Globe: Split decisions on school lottery.
Parents shut out of Boston pre-K classes despair, while others rejoice in top picks


"Chief Jasaad Rogers of Roxbury, like his brother before him, had lousy luck in the Boston public schools lottery. Not only was the 4-year-old shut out of the schools his parents wanted; he did not win a prekindergarten seat in any school at all. His parents, who both work full time, were left with few options besides paying for him to go somewhere else.
In West Roxbury, Debra Brendemuehl hit the jackpot, though she did not necessarily need full-day schooling for her 4-year-old, Brendan. (“They’re not kids forever,’’ she reasoned.)
She entered the lottery because she knew the only way to get him into the neighborhood’s highly sought-after schools was to apply when he was 4. The strategy worked: He won a spot at one of the city’s most competitive schools, the Lyndon in West Roxbury, which he can attend through eighth grade."

Sunday, April 24, 2011

Ad for custom egg donor

An ad in the Harvard Crimson (the student newspaper) reflects some of the fast-changing world of same-sex marriage and the market for reproductive services, with a mixed-race married gay couple looking for a Caucasian-Chinese mixed race egg donor. I infer that the market for surrogate wombs may also be involved.

**************

(This also reminds me of the work Kim Krawiec has been doing on the American Society for Reproductive Medicine’s guidelines for compensating oocyte donors. ("Total payments to donors in excess of $5,000 require justification and sums above $10,000 are not appropriate.")

Kim's recent blog posts on the subject are here, here, here and here, and her paper is here: Krawiec, Kimberly D., Sunny Samaritans and Egomaniacs: Price-Fixing in the Gamete Market (May 23, 2009). Law and Contemporary Problems, Vol. 72, No. 3, 2009; UNC Legal Studies Research Paper No. 1356012. Available at SSRN: http://ssrn.com/abstract=1356012

Saturday, April 23, 2011

Misc. repugnant transactions

Kung Pao Kitten (a recipe meant as a joke, that elicited lots of complaints...)



"A student who had sex with a girlfriend on top of a university building in front of hundreds of onlookers has been suspended from his fraternity."

"The university said it was investigating whether the actions of the male student "constituted a violation of university policies that prohibit unauthorised access to building roofs."

The university is USC.

Friday, April 22, 2011

Susan Athey and the National Medal of Science

No, not yet.
But this.

The White House

Office of the Press Secretary

For Immediate Release April 21, 2011 President Obama Announces More Key Administration Posts

Susan Athey, Appointee for Member, President’s Committee on the National Medal of Science
Susan Athey is a Professor of Economics at Harvard University and co-director of the Market Design Working Group at the National Bureau of Economic Research. Her current research studies the design of auction-based marketplaces, the statistical analysis of auction data, and internet economics. Dr. Athey was the first female recipient of the highly prestigious John Bates Clark medal, awarded by the American Economic Association, and she is a fellow of the American Academy of Arts and Sciences. She recently served as an elected member of the executive committee of the American Economics Association as well as the Council of the Econometric Society. Dr. Athey received her B.A. from Duke University in economics, mathematics, and computer science and her Ph.D. from the Stanford Graduate School of Business.

Laws against polygamy to be tested in Canada

Canadian laws against polygamy will be tested in a suit brought against some of the inhabitants of the rural enclave of Bountiful, British Columbia, who are polygamous adherents of the Fundamentalist Church of Jesus Christ of Latter Day Saints (FLDS). The Canadian magazine The Walrus covers the story: To the Exclusion of All Others: In a liberal society, is polygamy still intolerable?

At least part of the issue is how traditional divorce law, set up for dividing property between two people, would be adopted.
"American legal scholar Adrienne Davis, who believes that conventional family law rooted in monogamous marriage may not be up to attempts at cobbling polygamous marriage onto it, points out an alternative: commercial partnership law. Typically used when two or more parties go into business, according to Davis it would certainly address “polygamy’s central conundrum: ensuring fairness and establishing baseline behaviour in contexts characterized by multiple partners, on-going entrances and exits, and life-defining economic and personal stakes.” Of course, there would be a huge administrative cost to both adapting the model to marriage, and to ensuring that over the course of a union all partners consented to any new additions to it and renegotiated their respective rights as the landscape changed. More to the point, however, this is not what polygamists want, and it’s not what we want. Remember, liberal marriage was built on the concept of love; it’s hard to imagine a way of squaring this with the filing of an annual marriage report."

Thursday, April 21, 2011

Exploding offers and the market culture of law reviews

Here's an April 19 open letter To the legal community from a number of student-edited law journals.

"In recent years, many law journals have adopted the practice of issuing “exploding offers”—giving scholars only a couple of days, hours, or even minutes to accept an offer of publication. The reasoning behind these offers was simple: we each hoped to secure the best articles for our own journal before others could identify them and make competing offers. But experience has made clear that the costs of this practice—to the quality of our deliberations, to the faculty with whom we work, and, ultimately, to the scholarship we publish—dramatically outweigh the benefits. We therefore commit, effective immediately, to give every author at least seven days to decide whether to accept any offer of publication.

"This decision stems from the recognition that what once seemed an effective strategy for any one of us has in fact had a highly corrosive effect on all of us. Journals have responded to the prospect of exploding offers elsewhere by speeding up their own processes: rapidly winnowing down submissions, quickly holding articles committee votes, and, in the case of many journals, only occasionally consulting scholars in the field regarding an article’s novelty or contribution. This expedited review has inevitably favored established authors, popular topics, and broad claims at the expense of originality and merit. It has led many law journals to establish a twotrack process for article review: a fast track for widely recognized authors, whose submissions are more likely to elicit exploding offers; a slower track for younger authors and authors who teach at lower-ranked institutions. Many deserving pieces in the latter category never get to the front of the line.

"Moreover, expedited review has unduly compelled authors to undertake complicated workarounds and endure strong-arming and stress. Nor have exploding offers accomplished their purpose of improving our standing: for as often as we’ve taken good articles from others, we’ve had good articles taken from us. The dominant experience has merely been an ever-expanding push toward quick review and quick decision.

"Opening a seven-day offer window will substantially eliminate these defects. Student editors, lacking the incentive to expedite selection decisions, will be able to engage more deeply with the articles we review. We will have the time to consult scholars regularly regarding an article’s significance and novelty. As a result, all of us will be able to publish more of the stellar pieces that, under the current system, slip through the cracks.

"No doubt giving up a practice to which we’ve grown accustomed entails some risk. But we are confident that the risks of continuing the present race to the bottom are substantially greater. We invite all other student-edited law journals to join this letter, and we welcome an ongoing discussion with both journals and authors about how best to work together effectively."

HT: Clayton Featherstone, who writes "I wonder who the first defector will be?"

I notice that none of the journals signing the letter have made the more difficult promise not to respond to exploding offers from less prestigious journals. So there will still be incentives for authors to try to move up the prestige ranking of law journals by first soliciting offers from lower ranked journals, and then trying to turn these into hasty acceptances from higher ranked journals.

for more on exploding offers and market culture,
Niederle, Muriel, and Alvin E. Roth, "Market Culture: How Rules Governing Exploding Offers Affect Market Performance," American Economic Journal: Microeconomics, 1, 2, August 2009, 199-219.

And here are some (law review) articles on exploding offers in the market for law clerks:


  • Avery, Christopher, Christine Jolls, Richard A. Posner, and Alvin E. Roth, "The Market for Federal Judicial Law ClerksUniversity of Chicago Law Review, 68, 3, Summer, 2001, 793-902.(online at SSRN)



  • Avery, Christopher, Jolls, Christine, Posner, Richard A. and Roth, Alvin E., "The New Market for Federal Judicial Law Clerks" . University of Chicago Law Review, 74, Spring 2007, 447-486.
  • Wednesday, April 20, 2011

    A danceable economic experiment on public good provision

    Lights! Dancers! Economics!

    "If Milton Friedman and Martha Graham had a love child, it might look something like the "Tragedy of the Commons."

    "Antony Davies, an associate professor of economics at Duquesne University, and his sister, Jenefer Davies, an assistant professor of dance at Washington and Lee University, staged the experimental production this month at Washington and Lee to demonstrate a key principle of economics. The tragedy of the commons, enunciated in an essay of the same name in 1968 by the ecologist Garrett Hardin, states that when a resource is held jointly, its owners will deplete it more quickly than when individuals own equal and private portions of the same resource.
    ...
    "In the performance, five volunteers from the audience individually controlled spotlights that illuminated each of five dancers onstage. Volunteers were told that they should try to keep their dancers illuminated as long as possible but that the light was a limited resource: The first performance began with 30 seconds of light in the communal "light bank," and audience members drained that bank when they illuminated their dancers. Turning the light off, however, would slowly replenish the time in the bank.


    "Immediately after the first performance with the communal bank, the dancers began a second performance. But this time the five volunteers drew light from—and restored it to—private banks, up to six seconds per volunteer.
    ...
    "The economic theory played out as anticipated. The volunteers generated more light during the second leg of each of the three performances, with their individual "light banks," than they did while sharing time from the communal bank. Mr. Davies was relieved."

    You can see the dance here: econ dance performance