兩名美國學者獲諾貝爾經濟學獎
報道 2012年10月17日
周一，兩位美國人阿爾文·E·羅思(Alvin E.
Roth)和勞埃德·S·沙普利(Lloyd S.
Shapley)，因為在市場設計實踐和穩定匹配理論方面的貢獻獲得了諾貝爾經濟學獎。他們的研究關注的是如何儘可能有效地匹配不同市場主體，涉及的方面
包括婚姻、擇校、就業、器官捐贈等。
他們的研究主要應用於沒有價格的市場，或至少是對價格有着嚴格限制的市場。兩位得獎者的貢獻在於，在價格不能幫助購買者和銷售者實現匹配的情況下，如何適當地對人群和物資進行穩定分配。
今年60歲的羅思將這些理論運用到了實踐中，他開展了一個匹配新醫生和不同醫院的項目，最近還有一個匹配腎臟捐贈者的項目。紐約、波士頓、芝加哥和
丹佛的公立學校系統都採用了一套以他的研究為基礎的程序，將學生分配到不同學校。身為哈佛大學(Harvard
University)教授的羅思最近還接受了斯坦福大學(Stanford University)的一個職位。
“阿爾花了30年的時間試圖把經濟學變得更像一門工程設計學科，”麻省理工大學(MIT)的經濟學教授保勞格·帕塔克(Parag Pathak)說。他在校園匹配系統上與羅思進行過合作。“其指導理念就是，要弄清楚為什麼資源分配系統起不了作用，然後研究如何對它們進行重新設計，達 到更好的效果。”
89歲的沙普利是一名長期從事博弈論研究的數學家，也是加州大學洛杉磯分校(University of California, Los Angeles)的榮譽教授。20世紀50年代和60年代，他對市場設計和匹配理論的研究工作做出了一些最早的理論貢獻。
在1962年與戴維·蓋爾(David Gale)聯名發表的一篇論文中，沙普利解釋了不同個體如何能實現穩定配對，當時他們還對影響正確匹配的因素持有不同意見。這篇論文關注的是設計一個理想 而完美的穩定婚姻市場：能讓找尋配偶的雙方順利找到彼此，並且，已經結婚的人不會想（也不能夠）與原配偶分手，然後再與其他已婚的人結合。
20世紀80年代，羅思將該研究應用在了住院醫生實習項目中，後來又應用在選擇學校方面。他的研究興趣在於如何保持配對的公正性，以及如何防止更有經驗的參與者為了自己的利益而操縱系統。
他們的研究主要應用於沒有價格的市場，或至少是對價格有着嚴格限制的市場。兩位得獎者的貢獻在於，在價格不能幫助購買者和銷售者實現匹配的情況下，如何適當地對人群和物資進行穩定分配。
按圖放大
Jonathan Alcorn/Reuters, left, Linda A. Cicero/Stanford News Service, via Associated Press, right
美國科學家勞埃德·沙普利（左）和阿爾文·羅思，獲得了今年的諾貝爾經濟學獎。
“阿爾花了30年的時間試圖把經濟學變得更像一門工程設計學科，”麻省理工大學(MIT)的經濟學教授保勞格·帕塔克(Parag Pathak)說。他在校園匹配系統上與羅思進行過合作。“其指導理念就是，要弄清楚為什麼資源分配系統起不了作用，然後研究如何對它們進行重新設計，達 到更好的效果。”
89歲的沙普利是一名長期從事博弈論研究的數學家，也是加州大學洛杉磯分校(University of California, Los Angeles)的榮譽教授。20世紀50年代和60年代，他對市場設計和匹配理論的研究工作做出了一些最早的理論貢獻。
在1962年與戴維·蓋爾(David Gale)聯名發表的一篇論文中，沙普利解釋了不同個體如何能實現穩定配對，當時他們還對影響正確匹配的因素持有不同意見。這篇論文關注的是設計一個理想 而完美的穩定婚姻市場：能讓找尋配偶的雙方順利找到彼此，並且，已經結婚的人不會想（也不能夠）與原配偶分手，然後再與其他已婚的人結合。
20世紀80年代，羅思將該研究應用在了住院醫生實習項目中，後來又應用在選擇學校方面。他的研究興趣在於如何保持配對的公正性，以及如何防止更有經驗的參與者為了自己的利益而操縱系統。
From the Editor
Congratulations to Professor Al Roth, who this week was named a co-winner of the Nobel Prize in Economic Science for his Harvard Business School research on market design and matching theory. Roth's work and its importance are described quite nicely in the 2010 article by Carmen Nobel, How to Fix a Broken Marketplace.How to Fix a Broken Marketplace
| Published: | November 8, 2010 |
| Author: | Carmen Nobel |
Executive Summary:
Alvin E. Roth was a co-winner of the Nobel Prize in Economic Science this week for his Harvard Business School research into market design and matching theory. This article explores his research. Key concepts include:- Successful marketplaces must be "thick, uncongested, and safe."
- Sufficient "thickness" means there are enough participants in the market to make it thrive.
- "Congestion" is what can happen when markets get too thick too fast: there are heaps of potential players, but not enough time for transactions to be made, accepted, or rejected effectively.
- "Safety" refers to an environment in which all parties feel secure enough to make decisions based on their best interests, rather than attempts to game a flawed system.
About Faculty in this Article:
- More Working Knowledge from Alvin E. Roth
- Alvin E. Roth - Faculty
Research
- E-mail Alvin E. Roth: aroth@hbs.edu
As a Nobel Prize-winning pioneer in the field of market design, the Harvard Business School professor cofounded a kidney donation matching system for New England, corrected public school choice programs in New York and Boston, and tackled the market for new medical residents, economists, and lawyers. (Forbes magazine named him one of the world's "seven most powerful new economists.")
"Market design is the engineering part of game theory," Roth explains. "It's the underlying science of how the details work and how the parts fit together. We deal with much more complicated games than the game theory usually deals with."
In short, Roth has determined that successful marketplaces require three key elements. "They must be thick, uncongested, and safe," he says.
"Market design teaches us both about the details of market institutions and about the general tasks markets have to perform."Having sufficient "thickness" means there are enough participants in the market to make it thrive. "Congestion" is what can happen when markets get too thick too fast: there are heaps of potential players, but not enough time for transactions to be made, accepted, or rejected effectively. "Safety" refers to an environment in which all parties feel secure enough to make decisions based on their best interests, rather than attempts to game a flawed system.
Many markets must also overcome the fact that some transactions are considered repugnant, especially in the infancy of an industry. (For instance, life insurance—in which companies essentially place bets on when a customer will die—used to be considered extremely repugnant. But now it's a thriving industry.)
Roth discusses these and other markets in his reflective paper What Have We Learned from Market Design?, which draws from decades of his fieldwork. In the paper, published in 2008 and updated in September 2010, Roth discusses how issues of thickness, congestion, and safety impaired several important markets—and how market design made things better.
Thickness:
A classic example of a thickness problem is the process of helping nephrology patients in need of kidney transplants. In 2006, some 5,000 patients in the United States either died while on the waiting list for a new kidney or were removed from the list as "too sick to transplant," Roth says.
The system is rife with trouble. First of all, "there aren't enough deceased donors," Roth says. Second, while healthy people are able to live with a single kidney—and therefore able to donate one—it's illegal for them to sell one to a needy patient, owing to the aforementioned repugnance issue. Finally, those people willing to give up a kidney usually do so for a friend or relative, but those would-be donors often are incompatible with their intended recipient. "The problem with live donation is that you might not be able to give a kidney to the person you want to give to," Roth says.
Historically, those incompatible donors would be sent home, and their sick loved ones would wait for a deceased donor. But a few years ago Roth started studying the idea of a kidney exchange system: Say person A wants to give a kidney to person B, but their blood types don't match. Meanwhile, person C wants to give a kidney to person D, but their immune systems are incompatible. However, person A happens to be compatible with person D, and person C is compatible with person B. Each party has what the other party needs, creating a situation that economists call a "double coincidence of wants."
Roth found that while such exchanges did occur occasionally, which proved their feasibility, they were extremely rare prior to 2004. The market lacked thickness, due to a lack of recordkeeping. Because potential donors were not patients, there was no official record indicating that they might be available for a kidney exchange.
In 2004, he and fellow economists Tayfun Sönmez and M. Utku Ünver coauthored a paper showing that the kidney exchange market would benefit from an official clearinghouse that included a computerized database of incompatible patient-donor pairs. In addition to direct exchanges, the paper described exchanges that included three- and four-way matches—as well as a system in which a donor could give a kidney to a stranger in exchange for the donor's loved one receiving high priority on the cadaver waiting list.
"We deal with much more complicated games than the game theory usually deals with."They sent the paper to several kidney surgeons. The medical director of the New England Organ Bank met with Roth to pursue the idea further. This led to the founding of the New England Program for Kidney Exchange, which culls data from 14 transplant centers in the New England area, allowing incompatible donor pairs to find possible exchanges. So far, the program has been responsible for 73 successful exchanges. (Hospitals elsewhere have followed suit. Nationally, in 2005 there were 27 reported transplants involving an exchange; in 2007, there were121 such transplants; and in 2009, 304.)
"What would really help us have a thick market would be to have a well-organized national market," Roth says. "So far we're dealing with regional markets and trying to expand them."
Congestion:
When Roth and his colleagues were invited to improve the way New Yorkers are matched with high schools, they recognized a problem of market congestion. This is a common problem in markets where lots of parties are deciding whether to choose each other—first-year law firm jobs, for example, or competitive schools.
In New York City, public school students must apply to a high school of their choice, much as students in the rest of the country apply to private school. Each year, more than 90,000 students must be assigned to more than 500 high schools.
In the past, the system worked like this: The New York City Department of Education asked students to submit a ranked list of the five high schools they'd most like to attend, and the students would oblige. Next, the department would photocopy the list and send a copy to each of the five schools, which would then determine which students they wanted to accept, waitlist, or reject. Accepted students would decide whether to accept the schools back. Schools that still had vacancies could make a second round of offers and then a third. The process stopped after three rounds.
But there was a problem. The three rounds were not sufficient to assign every student to a school. Annually, while about 17,000 students would receive initial offers from multiple schools, about 50,000 received a single initial offer, and 30,000 were hastily shoved into schools that weren't on their choice list.
Administrators were well aware of where their schools ranked on each list, and some chose only those students who had ranked their school first. ("This meant you didn't really have five choices," Roth says.) Sometimes principals would withhold open slots, anticipating the chance to make late offers to high-achieving students who didn't like their initial assignments.
To solve the problem, Roth and his colleagues designed a "deferred acceptance algorithm." Rather than simultaneously apply to multiple schools, each student would apply to his or her highest ranked school. Each school would accept a set number of applicants and reject the rest, leaving room for the next round. Each student who didn't get into the first-choice school would apply to the second choice. This went on for up to 12 rounds.
In the first year of the new system, only about 3,000 students ended up in schools to which they didn't apply—and some of those were students who hadn't even submitted applications in the first place. The vast majority of students were accepted into one of their choices. "You might not get your first choice, but the system makes it safe to try; you can't do any better than to list your choices in their true order," Roth says.
Safety:
Meanwhile, the Boston Public Schools faced an issue of safety with its school choice system, although administrators were initially unaware of that. Ostensibly, the majority of prospective students in the city received their first-choice school, which led school officials to believe everything was fine. But it wasn't.
In the Boston system, students would send a ranked list to the city. (Unlike in New York, Boston did not include administrators of individual schools in the process.) The central administration tried to assign a first-choice school to as many students as possible, with priority given to students whose siblings already attended the school or who lived within its "walk zone." For each school with slots still available, the city would assign a round of second choices, and so on.
The problem was that a student who didn't get into a first-pick school wasn't likely to get into a second-pick school either, because that second-pick school would already be full of students who had listed it as a first pick. "That meant it might be too risky to choose your first choice," Roth says.
Savvy students and parents knew to avoid listing the very best schools as their first choice. After all, only kids with priority at that school were likely to get into that school anyway. But not everyone was savvy. Some 19 percent of applicants did list over-demanded schools as their top two choices—and 27 percent of those ended up without an assignment at all. And many of those who did receive their first choices were unhappy because their choices were strategic, rather than honest.
Roth and his colleagues recommended two design algorithms that were essentially strategy-proof, making it safe and reasonable for students to apply to the schools that they honestly wanted most. The Boston School Committee adopted the proposal.
Roth also has helped design markets to match new doctors with residency programs and new economists with new jobs. Lately, he has been looking at the market for new lawyers, in which law school students compete for the best jobs and firms compete for the best students in a very tight economy. In order to beat the competition, firms are offering jobs to students before they even begin their second year of law school—and demanding that the students decide immediately. This leads to a safety issue, in which both a student and a firm are committing to a decision before either has a real inkling of what kind of lawyer the student will become in two years.
"Market design teaches us both about the details of market institutions and about the general tasks markets have to perform," Roth writes in "What Have We Learned from Market Design?" "Among the general tasks markets have to perform, difficulties in providing thickness, dealing with congestion, and making participation safe and simple are often at the root of market failures that call for new market designs."
For more information on market design, please visit Market Design, a blog Roth coauthors with HBS professor Peter Coles.
FT:
2012年諾貝爾經濟學獎被授予美國學者阿爾文•羅思(Alvin Roth)和勞埃德•沙普利(Lloyd Shapley)，以表彰他們在“如何讓不同人為了互惠互利而走到一起”這個課題上的獨立研究。從閃電約會活動，到分配中學招生名額，他們的研究成果構成了很多事情的理論基礎。瑞典央行(Riksbank)將這個紀念阿爾弗雷德•諾貝爾(Alfred Nobel)的獎項授予上述美國學者，獎勵他們的抽象理論研究，也獎勵他們努力將這些研究成果應用於實踐。諾貝爾委員會此舉也使其避免在圍繞危機、緊縮和財政政策的宏觀經濟辯論中站在任何陣營，因為這兩位得主的經濟學研究領域與這場辯論相距甚遠。相反，這個決定體現了找到一個重要研究領域，把諾貝爾經濟學獎授予其中幾名領軍人物（即便他們從未在一起合作）的傳統。加州大學洛杉磯分校(UCLA)的沙普利教授現年89歲，他之所以獲獎是因為他在合作博弈論領域進行的研究，尤其是如何在不同人或不同群體之間找到穩定匹配，使這些人或群體不希望與現有夥伴以外的任何一方交易或打交道，在這些領域，簡單的市場規則並不適用。“我自認為是個數學家，而這個獎是經濟學獎，”他對美聯社(AP)表示。 “我一輩子沒有學過經濟學課程。”哈佛大學(Harvard University)的羅思教授現年60歲，他在實驗室實驗中採用沙普利教授的研究成果，並在實踐中將其用於在醫生與醫院、器官捐獻者與患者、學生與學校之間實現匹配。羅思教授表示，他在加州的居所接到午夜電話，“意外”和“驚喜地”獲知他已得獎。 “過去一個小時裡，我主要的慶祝方式是在電話裡講話，”他對路透社(Reuters)表示，“我希望生活不久就會恢復正常。”對多數市場而言，面對近乎無限的需求，供應有限的物資（例如電視機、茄汁焗豆，或者橙子）如何分配這個問題，是由價格機制解決的。價格使供給和需求達到平衡，但在很多領域，在分配其它稀缺事物方面不存在市場。在收學費不合法或者學費有上限的情況下分配學校招生名額，或者在基於倫理的法律禁止金錢交易的情況下向需要器官移植的人分配人體組織，要找到這些場合的最佳分配方式，難度都大得多。沙普利教授在上世紀50和60年代對這些市場的穩定合作匹配進行了理論研究。一個穩定匹配的定義是，在有許多可能選擇的時候，雙方都認為尋求別的匹配沒有益處的那一對匹配。在實踐中，這個問題的第一個、同時也是最出名的實例是找到婚姻伴侶。沙普利教授在1962年與戴維•蓋爾(David Gale)合寫的一篇論文中，提出一種在10名男士和10名女士之間找到穩定伴侶的理論方法，按照這種方法，沒有一個男士或女士會尋求與伴侶分手，轉而與別人相好。其過程是，由男士們或女士們選擇他（她）們最喜歡的人（這種方式如今應用於閃電約會）。如果由女士們選擇，那麼被選中的男士將挑選自己的第一選擇，在第一輪沒有找到伴侶的女士們將投入第二輪，即從剩下來的男士中進行選擇。蓋爾和沙普利教授從數學上證明，這個過程將帶來穩定匹配。兩名作者在這個例子中也顯示，哪一方得到選擇的權利是重要的。與被選擇的性別相比，作出選擇的那個性別更快樂，並得到更好的結局。匹配理論的其它應用場合是由羅思教授設計的，它們包括找到實習醫生與不同醫院、學生與學校、腎臟與患者之間的最佳匹配方式。為子女挑選倫敦的中學或美國許多城市的中小學的父母，都獲益於羅思教授對蓋爾-沙普利算法(
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如果我從未聽說過今年諾貝爾經濟學獎的兩位得主：勞埃德•沙普利(Lloyd Shapley)和阿爾文•羅思(Alvin Roth)，我該不該為此煩惱？完全沒有必要。大多數學者型經濟學家都埋頭自己的工作，他們的名字並不為大眾所知。今年的諾貝爾獎旨在表彰經濟學家們日復一日所做的有益研究，而非力求選出一位成就最高、能力最強的經濟學家。今年的諾獎肯定了經濟學家為理解生活中的棘手問題並找到能使人們變得更愉快的最優機制所做的努力。沙普利和羅思找到的並不是關於生命、宇宙和萬事萬物的答案，而只是改善我們自我組織方式的漸進式辦法。我們已然有了食品市場、衍生品市場等各類市場，他們所研究的“匹配機制”還有什麼意義？不管你是否相信，很多事情並不是由價格充當供求調節槓桿的市場決定的。尋找合作夥伴、送孩子進學校讀書、加入腎臟移植等待名單……這些事情與掏錢購買橙子幾乎沒有共同點，但它們的模式已足夠成熟，可以用做研究。理性的人在這些事情上會如何抉擇並得到合意的結果呢？這就是沙普利和羅思研究的問題。上世紀50年代至60年代，沙普利從理論和數學的角度進行了研究；羅思教授則在近些年將前者得出的理論應用於實際。如果我要選擇學校或尋找夥伴，我只需陳述自己的偏好，是這樣嗎？錯。在某些情況下，你確實可以這麼做。但是，無論你如何陳述，最終能夠決定結果的都將是制度環境。例如上世紀80年代時，我曾想去劍橋大學(Cambridge University)讀經濟學。在劍橋的幾所學院當中，我有一些屬意的對象，但我所在的學校不允許我申請其中的一所，因為當時還有另一名學生也在申請這所學院。我還陳述了我認為各個學院多麼的受歡迎以及它們素以招收像我這樣的學生而聞名，以求盡量增大自己被錄取的概率。但最終，我所陳述的偏好不過是一次試圖和整個體制博弈的嘗試。沙普利和羅思的研究成果給我們帶來了什麼？你參加過“快速相親”活動嗎？這個配對過程就是對蓋爾-沙普利(Gale-Shapley)“延遲接受”(deferred acceptance)程序的一次運用。或者，你是否有孩子、並且和孩子住在倫敦、紐約或波士頓？如果你想讓他們在公立學校中接受教育，目前的擇校算法就是由羅思設計的。這種新的選擇機制鼓勵家長們陳述自己的真實偏好。在紐約，這種擇校算法的引入，使得沒能被自己所選任一學校錄取的學生人數從2002年的3萬名降至2003年的3000名，降幅達90%。聽起來挺簡單的……是的——當該理論及其應用為人們所理解時確實如此。但直到近期，這些匹配機制才被用於改善我們的生活。因此，要說服我們不再使用不夠穩定的匹配機制，顯然需要聰明的頭腦。譯者/馬拉
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