Introduction to Market Design,ECON 285 – 01

Autumn Quarter 2012Professors Muriel Niederle and Al Roth

Introduction to market design... will emphasize the combined use of economic theory, experiments and empirical analysis to analyze and engineer market rules and institutions.

In this first quarter we will pay particular attention to matching markets, which are those in which price doesn’t do all of the work, and which include some kind of application or selection or assignment process.

Market designers have participated in the design and implementation of a number of marketplaces, and the course will emphasize the relation between theory and practice.

We’ll also discuss various forms of market failure. 2

Some useful websites• Course web page: for syllabus, including links to

reading, and for weekly handouts (including these slides):(we’ll email you a link as soon as it’s ready, and before next week)

• My market design web page (for general background and papers—soon to move to a Stanford URL): http://kuznets.fas.harvard.edu/~aroth/alroth.html

• Market design blog: http://marketdesigner.blogspot.com/

3

Assignment• One final paper. The objective of the final paper is to

study an existing market or an environment with a potential role for a market, describe the relevant market design questions, and evaluate how the current market design works and/or propose improvements on the current design.– In the past, these have varied widely; some have been

explorations of mathematical models, some have been full of institutional description…

• We’ll ask you for brief descriptions of your preliminary ideas from time to time.

• The Market Design blog is intended in part to help generate ideas.

• We may occasionally assign some exercises

4

Recommended text (for the early part of the class)

• Roth, Alvin E. and Marilda Sotomayor Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis, Econometric Society Monograph Series, Cambridge University Press, 1990. (get the paperback edition.)

• Any ‘housekeeping’ questions about the class?

5

Lightning overview of the course

• Design is both a verb and a noun, and we’ll approach market design both as an activity and as an aspect of markets that we study.

• The course will have both substantive and methodological themes.

• Design also comes with a responsibility for detail. Designers can’t be satisfied with simple models that explain the general principles underlying a market; they have to be able to make sure that all the detailed parts function together. 6

Methodology• Responsibility for detail requires the ability to

deal with complex institutional features that may be omitted from simple models.

• Game theory, the part of economics that studies the “rules of the game,” provides a framework with which design issues can be addressed.

• But dealing with complexity will require new tools, to supplement the analytical toolbox of the traditional theorist.

7

• Game Theory, experimentation, and

computation, together with careful observation of historical and contemporary markets (with particular attention to the market rules), are complementary tools of Design Economics

• Computation helps us find answers that are beyond our current theoretical knowledge.

• Experiments play a role – In diagnosing and understanding market failures, and

successes– In designing new markets– In communicating results to policy makers

8

An analogy• Consider the design of suspension bridges. Their simple

physics, in which the only force is gravity, and all beams are perfectly rigid, is simple, beautiful and indispensable.

• But bridge design also concerns metal fatigue, soil mechanics, and the sideways forces of waves and wind. Many questions concerning these complications can’t be answered analytically, but must be explored using physical or computational models.

• These complications, and how they interact with that part of the physics captured by the simple model, are the concern of the engineering literature. Some of this is less elegant than the simple model, but it allows bridges designed on the same basic model to be built longer and stronger over time, as the complexities and how to deal with them become better understood.

9

• In this class, the simple models will be models of

matching.

• In recent years there have been some great advances in the theory of matching, including developments that bring matching and auction models together.

• A lot of these theoretical insights have come from the difficulties faced in designing complex labor markets and auctions (e.g. labor markets in which there may be two-career households, and auctions in which bidders may wish to purchase packages of goods).

10

11

Substantive lessons from market failures and successes

• To achieve efficient outcomes, marketplaces need make markets sufficiently– Thick

• Enough potential transactions available at one time• (We’ll spend some time talking about how markets sometimes

unravel)– Uncongested

• Enough time for offers to be made, accepted, rejected…– Safe

• Safe to act straightforwardly on relevant preferences

• Some kinds of transactions are repugnant…– This can be an important constraint on market design

12

Some examples• Medical labor markets

– NRMP in 1995 (thickness, congestion, incentives)– Gastroenterology in 2006 (thickness, incentives)

• Is reneging on early acceptances repugnant?• School choice systems:

– New York City since Sept. 2004 (congestion & incentives)– Boston since Sept. 2006 (incentives)

• Repugnant: exchange of priorities (particularly sibling priorities)– Denver, D.C. and New Orleans since Sept 2012

• Kidney exchange (thickness, congestion, incentives)– New England and Ohio (2005), other grass-roots networks– National US (piloting since 2010??)

• Repugnant: monetary markets• American market for new economists

– Scramble (thickness) March 2006– Signaling (congestion) December 2007

Some of these markets use money, and some don’t

Section 301 of the National Organ Transplant Act

(NOTA), 42 U.S.C. 274e 1984 states:

“it shall be unlawful for any person to knowingly

acquire, receive or otherwise transfer

any human organ for valuable consideration

for use in human transplantation”.

13

14

A classic economic problem: Coincidence of wants

(Money and the Mechanism of Exchange, Jevons 1876)

Chapter 1: "The first difficulty in barter is to find two persons whose disposable possessions mutually suit each other's wants. There may be many people wanting, and many possessing those things wanted; but to allow of an act of barter, there must be a double coincidence, which will rarely happen. ... the owner of a house may find it unsuitable, and may have his eye upon another house exactly fitted to his needs. But even if the owner of this second house wishes to part with it at all, it is exceedingly unlikely that he will exactly reciprocate the feelings of the first owner, and wish to barter houses. Sellers and purchasers can only be made to fit by the use of some commodity... which all are willing to receive for a time, so that what is obtained by sale in one case, may be used in purchase in another. This common commodity is called a medium, of exchange..."

Let’s start with medical labor markets

• They use money (doctors are paid), but they are prototypical matching markets…

15

16

Matching doctors to first positions in U.S. and Canada

• The redesign in 1995 of the– U.S. National Resident Matching Program (NRMP)

(approx. 23,000 positions, 500 couples)– Canadian Resident Matching Service (CaRMS)

(1,400 Canadian medical grads, including 41 couples, 1,500 positions in 2005)

• The redesign in 2005 of the fellowship market for Gastroenterologists– Contemporary issues in labor markets for

Orthopaedic surgeons, neuropsychologists, and law clerks for appellate judges.

17

Background to redesign of the medical clearinghouses

• 1900-1945 UNRAVELLING OF APPOINTMENT DATES• 1945-1950 CHAOTIC RECONTRACTING--Congestion• 1950-197x HIGH RATES OF ORDERLY PARTICIPATION

( 95%) in centralized clearinghouse• 197x-198x DECLINING RATES OF PARTICIPATION

(85%) particularly among the growing number of MARRIED COUPLES

• 1995-98 Market experienced a crisis of confidence with fears of substantial decline in orderly participation; – Design effort commissioned—to design and compare alternative

matching algorithms capable of handling modern requirements: couples, specialty positions, etc.

– Roth-Peranson clearinghouse algorithm adopted, and employed

18

Stages and transitions observed in various markets

Stage 1: UNRAVELINGOffers are early, dispersed in time, exploding…no thick market

Stage 2: UNIFORM DATES ENFORCEDDeadlines, congestion

Stage 3: CENTRALIZED MARKET CLEARING PROCEDURES

19

What makes a clearinghouse successful or unsuccessful?

• A matching is “stable” if there aren’t a doctor and residency program, not matched to each other, who would both prefer to be.

• Hypothesis: successful clearinghouses produce stable matchings.

• How to test this?

20

Gale, David and Lloyd Shapley [1962], Two-Sided Matching Model

Men = {m1,..., mn} Women = {w1,..., wp}

PREFERENCES (complete and transitive):– P(mi) = w3, w2, ... mi ... [w3 >mi w2]

– P(wj) = m2, m4, ... wj ...

Outcomes= matchings: :MW MW – such that w = (m) iff (w)=m, – And either (w) is in M or (w) = w, and – either (m) is in W or (m) = m

21

Stable matchingsA matching is • BLOCKED BY AN INDIVIDUAL k if k prefers being single to

being matched with (k), i.e. k >k (k) ((k) is unacceptable).

• BLOCKED BY A PAIR OF AGENTS (m,w) if they each prefer each other to , i.e.

• w >m (m) and m >w (w)• A matching is STABLE if it isn't blocked by any individual or

pair of agents.• NB: A stable matching is efficient, and in the core, and in this

simple model the set of (pairwise) stable matchings equals the core.

22

GS Deferred Acceptance Algorithm, with men proposing

• 1 a. Each man m proposes to his 1st choice (if he has any acceptable choices).

• b. Each woman rejects any unacceptable proposals and, if more than one acceptable proposal is received, "holds" the most preferred and rejects all others.

• k a. Any man rejected at step k-1 makes a new proposal to its most preferred acceptable mate who hasn’t yet rejected him. (If no acceptable choices remain, he makes no proposal.)

• b. Each woman holds her most preferred acceptable offer to date, and rejects the rest.

• STOP: when no further proposals are made, and match each woman to the man (if any) whose proposal she is holding.

Example

M = {m1, m2, m3}, W = {w1, w2, w3} P(m1) = w2,w1,w3 P(w1) = m1,m2,m3P(m2) = w1,w2,w3 P(w2) = m3,m1,m2P(m3) = w1,w2,w3 P(w3) = m1,m2,m3 M = ([m1,w1], [m2,w3], [m3,w2]) = W

23

24

GS’s Remarkable Theorem (1st of 2)

• Theorem 1 (GS): A stable matching exists for every marriage market.

Another kind of matching algorithm: Priority matching • Edinburgh, 1967 No longer in use• Birmingham 1966, 1971, 1978 " " " "• Newcastle 1970's " " " "• Sheffield 196x " " " "

In a priority matching algorithm, a 'priority' is defined for each firm-worker pair as a function of their mutual rankings. The algorithm matches all priority 1 couples and removes them from the market, then repeats for priority 2 matches, priority 3 , etc.

E.g. in Newcastle, priorities for firm-worker rankings were organized by the product of the rankings, (initially) as follows: 1-1, 2-1, 1-2, 1-3, 3-1, 4-1, 2-2, 1-4, 5-1...

Is it stable? 25

Priority matching (an unstable system) • This can produce unstable matchings -- e.g. if a desirable firm and worker

rank each other 4th, they will have such a low priority (4x4=16) that if they fail to match to one of their first three choices, it is unlikely that they will match to each other. (e.g. the firm might match to its 15th choice worker, if that worker has ranked it first...)

• After 3 years, 80% of the submitted rankings were pre-arranged 1-1 rankings without any other choices ranked. This worked to the great disadvantage of those who didn't pre-arrange their matches.

26

27

Market Stable Still in use (halted unraveling)

• NRMP yes yes (new design in ’98)• Edinburgh ('69) yes yes• Cardiff yes yes• Birmingham no no• Edinburgh ('67) no no• Newcastle no no• Sheffield no no• Cambridge no yes• London Hospital no yes• Medical Specialties yes yes (~30 markets, 1 failure)• Canadian Lawyers yes yes (Alberta, no BC, Ontario)• Dental Residencies yes yes (5 ) (no 2)• Osteopaths (< '94) no no• Osteopaths (> '94) yes yes• Pharmacists yes yes• Reform rabbis yes (first used in ‘97-98) yes• Clinical psych yes (first used in ‘99) yes

Stability looks like an important criterion for a successful clearinghouse.

28

The need for experiments

• How to know if the difference between stable and unstable matching mechanisms is the key to success?– There are other differences between e.g.

Edinburgh and Newcastle• The policy question is whether the new

clearinghouse needs to produce stable matchings (along with all the other things it needs to do like handle couples, etc. )– E.g. rural hospital question…

29

A matching experiment(Kagel and Roth, QJE 2000)

• 6 firms, 6 workers (half "High productivity" half "low productivity")• It is worth $15 plus or minus at most 1 to match to a high• It is worth $5 plus or minus at most 1 to match to a low• There are three periods in which matches can be made:-2, -1, 0.• Your payoff is the value of your match, minus $2 if made in • period -2, minus $1 if made in period -1• Decentralized match technology : firms may make one offer at any

period if they are not already matched. Workers may accept at most one offer. Each participant learns only of his own offers and responses until the end of period 0.

• After experiencing ten decentralized games, a centralized matching technology was introduced for period 0 (periods -2 and -1 were organized as before).

• Centralized matching technology: participants who are still unmatched at period 0 submit rank order preference lists, and are matched by a centralized matching algorithm.

• Experimental variable: Newcastle (unstable) or Edinburgh (stable) algorithm.

30

Average Cost of Early Markets

0

2

4

6

8

10

1-5 6-10 11-15 16-20 21-25

Markets #

Co

st

(Do

llars

)

Decentralized Markets Markets with a Clearinghouse

Stable (Deferred

Acceptance) algorithm

New castlePriority

algorithm

31

Offers and acceptances

32

Market Stable Still in use (halted unraveling)

• NRMP yes yes (new design in ’98)• Edinburgh ('69) yes yes• Cardiff yes yes• Birmingham no no• Edinburgh ('67) no no• Newcastle no no• Sheffield no no• Cambridge no yes• London Hospital no yes• Medical Specialties yes yes (~30 markets, 1 failure)• Canadian Lawyers yes yes (Alberta, no BC, Ontario)• Dental Residencies yes yes (5 ) (no 2)• Osteopaths (< '94) no no• Osteopaths (> '94) yes yes• Pharmacists yes yes• Reform rabbis yes (first used in ‘97-98) yes• Clinical psych yes (first used in ‘99) yes• Lab experiments yes yes.(Kagel&Roth QJE 2000) no no

Lab experiments fit nicely on the list, just more of a variety of observations that increase our confidence in the robustness of our conclusions, the lab observations are the smallest but most controlled of the markets on the list…

33

Current NRMP match (Roth/Peranson algorithm)

Produces “student optimal” stable matching (as close as can be given match complications)

• Deals with major match complications– Married couples

• They can submit preferences over pairs of positions– Applicants can match to pairs of jobs, PGY1&2

• They can submit supplementary preference lists– Reversions of positions from one program to

another• The algorithm starts as a student (and couple)- proposing

deferred acceptance algorithm, and then resolves instabilities with an algorithm modeled on the Roth-Vande Vate (1990) blocking-pair-satisfying algorithm (which arose in part in response to an open problem by Knuth…)

34

Stable Clearinghouses (those now using the Roth Peranson Algorithm)

NRMP / SMS:Medical Residencies in the U.S. (NRMP) (1952)Abdominal Transplant Surgery (2005) Child & Adolescent Psychiatry (1995) Colon & Rectal Surgery (1984) Combined Musculoskeletal Matching Program (CMMP) • Hand Surgery (1990) Medical Specialties Matching Program (MSMP) • Cardiovascular Disease (1986)

• Gastroenterology (1986-1999; rejoined in 2006)

• Hematology (2006) • Hematology/Oncology (2006) • Infectious Disease (1986-1990; rejoined in 1994) • Oncology (2006) • Pulmonary and Critical Medicine (1986) • Rheumatology (2005) Minimally Invasive and Gastrointestinal Surgery (2003) Obstetrics/Gynecology • Reproductive Endocrinology (1991) • Gynecologic Oncology (1993) • Maternal-Fetal Medicine (1994) • Female Pelvic Medicine & Reconstructive Surgery (2001) Ophthalmic Plastic & Reconstructive Surgery (1991) Pediatric Cardiology (1999) Pediatric Critical Care Medicine (2000) Pediatric Emergency Medicine (1994) Pediatric Hematology/Oncology (2001) Pediatric Rheumatology (2004) Pediatric Surgery (1992)

Primary Care Sports Medicine (1994)Radiology • Interventional Radiology (2002) • Neuroradiology (2001) • Pediatric Radiology (2003) Surgical Critical Care (2004) Thoracic Surgery (1988) Vascular Surgery (1988)

Postdoctoral Dental Residencies in the United States• Oral and Maxillofacial Surgery (1985)• General Practice Residency (1986)• Advanced Education in General Dentistry (1986)• Pediatric Dentistry (1989)• Orthodontics (1996)Psychology Internships in the U.S. and CA (1999)Neuropsychology Residencies in the U.S. & CA (2001)Osteopathic Internships in the U.S. (before 1995)Pharmacy Practice Residencies in the U.S. (1994)Articling Positions with Law Firms in Alberta, CA(1993)Medical Residencies in CA (CaRMS) (before 1970)

********************British (medical) house officer positions• Edinburgh (1969)• Cardiff (197x)

New York City High Schools (2003)Boston Public Schools (2006)

Market Design Manifesto

• We need to understand how markets work well enough to fix them when they’re broken.

35

Homework exercise• Here is the web site of the American Association of Colleges of

Podiatric Medicine http://www.casprcrip.org/html/casprcrip/students.asp

• They run a match, and here is the description of their algorithm: http://www.casprcrip.org/html/casprcrip/pdf/MatchExpl.pdf

• Is their algorithm equivalent to the hospital proposing deferred acceptance procedure?– Does it produce the same matching, when it produces a matching?– Does it always (for every preference profile) produce a matching?– Is the description of the algorithm complete enough to be sure?

• Come prepared to give an answer at the beginning of next class… (note that the podiatry algorithm is a many-to-one match like the college admissions problem, not a one-to-one match like the marriage problem—you may want to look ahead in the notes…)

36

Syllabus Econ 285, Market Design, Niederle and Roth, Autumn 2012 (subject to revision, this version 9/25/12:)

1. 24 Sept: Introduction to market design1. No class 26 Sept (Yom Kippor)

2. 1 October: Theory of Stable matchings 13. 3 October: Theory of Stable matchings 24. 8 October: NRMP design, couples, 5. 10 October: congestion and Signaling (APPIC and AEA)6. 15 October: Generalized matching (Hatfield and Ostrovsky?)7. 17 October: Kidney exchange 18. 22 October: Kidney exchange 29. 24 October: Unraveling and gastro 110. 29 October: Unraveling 211. 31 October School choice12. 5 November School choice 213. 7 November: School choice, Guillaume Haeringer14. 12 November Schools and slots: Scott Kominers 15. 14 November: Random assignment mechanisms16. 26 November: ?Rank efficiency (Clayton?)17. 28 November: Another visitor (Nikhil?)18. 3 December: Student presentations19. 5 December: Student presentations 37

Matching is important

38

39

Midrash Rabbah (VaYikra Rabbah)Translated into English under the editorship of Rabbi Dr. H. Freedman, and Maurice Simon,Leviticus, Chapters I-XIX translated by Rev. J. Israelstam, Soncino Press, London, 1939Chapter VIII (TZAV)

A Roman lady asked R. Jose b. Halafta: ‘In how many days did the Holy One, blessed be He, create His world”’ He answered: ‘In six days, as it is written, For in six days the Lord made heaven and earth, etc.(Ex. XXXI, 17). She asked further: ‘And what has He been doing since that time?’ He answered: ‘He is joining couples [proclaiming]: “A’s wife [to be] is allotted to A; A’s daughter is allotted to B; (So-and-so’s wealth is for So-and-so).”’1 Said she: ‘This is a thing which I, too, am able to do. See how many male slaves and how many female slaves I have; I can make them consort together all at the same time.’ Said he: ‘If in your eyes it is an easy task, it is in His eyes as hard a task as the dividing of the Red Sea.’ He then went away and left her. What did she do? She sent for a thousand male slaves and a thousand female slaves, placed them in rows, and said to them: ‘Male A shall take to wife female B; C shall take D and so on.’ She let them consort together one night. In the morning they came to her; one had a head wounded, another had an eye taken out, another an elbow crushed, another a leg broken; one said ‘I do not want this one [as my husband],’ another said: ‘I do not want this one [as my wife].’

1. M.K. deletes this as irrelevant. But E.J. explains: A’s wealth is to be given to B, as a dowry for the former’s daughter.

40

Speaking of which…

• We won’t hold class on Wednesday• It is Yom Kippor, the end of the celebration of

the beginning of the Jewish New Year, 5773.• So our next class will be next week, Monday,

October 1.

41