Introduction to Market Design,Econ 2056a and Business 4150:

Professors Al Roth and Peter Coles, Fall 2008

Some useful websites

• Course web page: for syllabus, including links to reading, and for weekly handouts (including these slides): http://my.harvard.edu/icb/icb.do?keyword=k40018

• My market design web page (for general background and papers): http://kuznets.fas.harvard.edu/~aroth/alroth.html

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

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 insitutional 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.

Recommended texts• 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.)

• Milgrom, Paul "Putting Auction Theory to Work" by Paul Milgrom (Churchill Lectures), Cambridge University Press, 2004

• Klemperer, Paul "Auctions: Theory and Practice" (Toulouse Lectures), Princeton University Press, 2004.

Lightning overview of the course(Peter will continue the overview next week when he’s back.)

• 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.

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.

• 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

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.

• In this class, the simple models will be models of matching, and of auctions.

• In recent years there have been some great advances in the theory of each of these, that brings them much closer 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).

• (Paul Milgrom and his colleagues have led the way on much of the recent theoretical work.)

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Substantive lessons from market failures and successes

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

• Enough potential transactions available at one time

– 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

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Some examples• Kidney exchange (thickness, congestion, incentives)

– New England and Ohio (2005)– National US (2007?)

• Repugnant: monetary markets• School choice systems:

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

• Repugnant: exchange of priorities (particularly sibling priorities)• American market for new economists

– Scramble ((thickness)– Signaling (congestion)

• Medical labor markets – NRMP in 1995 (thickness, congestion, incentives)– Gastroenterology in 2006 (thickness, incentives)

• Is reneging on early acceptances repugnant?

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Kidney exchange--background• There are over 75,000 patients on the waiting list

for cadaver kidneys in the U.S. • In 2007 32,452 patients were added to the waiting

list, and 25,879 patients were removed from the list.

• In 2007 there were 10,587 transplants of cadaver kidneys performed in the U.S.

• In the same year, 4,472 patients died while on the waiting list (and more than 1,300 others were removed from the list as “Too Sick to Transplant”.

• In 2007 there were also 6,039 transplants of kidneys from living donors in the US.

• Sometimes donors are incompatible with their intended recipient.

• This opens the possibility of exchange .

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Donor 1Blood type A

Recipient 1Blood type B

Donor 2Blood type B

Recipient 2Blood type A

Simple Two Pair Kidney Exchange

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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”.

Legal opinion obtained by the transplant community interprets

this has forbidding buying and selling, but allowing exchange.

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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..."

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Kidney exchange clearinghouse designRoth, Alvin E., Tayfun Sönmez, and M. Utku Ünver, “Kidney Exchange,”

Quarterly Journal of Economics, 119, 2, May, 2004, 457-488. ________started talking to docs____________ “Pairwise Kidney Exchange,” Journal of Economic Theory, 125, 2, 2005,

151-188.___ “A Kidney Exchange Clearinghouse in New England,” American Economic

Review, Papers and Proceedings, 95,2, May, 2005, 376-380._____ “Efficient Kidney Exchange: Coincidence of Wants in a Structured

Market,” American Economic Review, forthcomingSaidman, Susan L., Alvin E. Roth, Tayfun Sönmez, M. Utku Ünver, and

Francis L. Delmonico, “Increasing the Opportunity of Live Kidney Donation By Matching for Two and Three Way Exchanges,” Transplantation, 81, 5, March 15, 2006, 773-782.

Roth, Alvin E., Tayfun Sönmez, M. Utku Ünver, Francis L. Delmonico, and Susan L. Saidman, “Utilizing List Exchange and Undirected Donation through “Chain” Paired Kidney Donations,” American Journal of Transplantation, 6, 11, November 2006, 2694-2705.

And in the medical literature

Saidman, Susan L., Alvin E. Roth, Tayfun Sönmez, M. Utku Ünver, and Francis L. Delmonico, “Increasing the Opportunity of Live Kidney Donation By Matching for Two and Three Way Exchanges,” Transplantation, 81, 5, March 15, 2006, 773-782.

Roth, Alvin E., Tayfun Sönmez, M. Utku Ünver, Francis L. Delmonico, and Susan L. Saidman, “Utilizing List Exchange and Undirected Donation through “Chain” Paired Kidney Donations,” American Journal of Transplantation, 6, 11, November 2006, 2694-2705.

Rees, Michael A., Jonathan E. Kopke, Ronald P. Pelletier, Dorry L. Segev, Matthew E. Rutter, Alfredo J. Fabrega, Jeffrey Rogers, Oleh G. Pankewycz, Janet Hiller, Alvin E. Roth, Tuomas Sandholm, Utku Ünver, and Robert A. Montgomery, “The First Never-Ending Altruistic Donor Chain,” April, 2008.

Rees, Michael A., Alvin E. Roth, Tuomas Sandholm, M Utku Unver, Ruthanne Hanto, and Francis L. Delmonico, “Designing a National Kidney Exchange Program,” April, 2008.

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There’s also a growing CS literature• Abraham, D., Blum, A., and Sandholm, T. 2007. Clearing

Algorithms for Barter Exchange Markets: Enabling Nationwide Kidney Exchanges. In Proceedings of the ACM Conference on Electronic Commerce (EC).

• Cechlarova, Katarina, Tamas Fleiner, and David Manlove [2005], "The Kidney Exchange Game," Proc. SOR '05 (2005), Eds. L. Zadnik-Stirn, S. Drobne, 77-83.

• K. Cechlarova, V. Lacko, The kidney exchange problem: How hard is it to find a donor? IM Preprint (2006) 4/2006

• Péter Biró, Katarína Cechlárová: Inapproximability of the kidney exchange problem. Inf. Process. Lett. 101(5): 199-202 (2007)

• Borbel’ova, Viera and Katarina Cechlarova: “Pareto Optimality in the kidney exchange game,”

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Objectives of a kidney exchange• Thick market: assemble database of incompatible

patient-donor pairs– New England Program for Kidney Exchange (2005)– Alliance for Paired Donation (2006)– National matching under discussion

• Find efficient feasible matchings, in an “incentive compatible” way (i.e. in a way that makes it safe for everyone to reveal their private information and go ahead with the resulting exchanges). – Prime incentive issues:

• All transplants in an exchange performed simultaneously• transplant centers that can do a local exchange should

nevertheless submit pairs to the regional/national exchange.

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Incentives: 2-way exchange involves 4 simultaneous surgeries.

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The exchange P1-P2 results in two transplantations, but the exchanges P1-P4 and P2-P3 results in four.

So even if Pairs 1 and 2 are at the same transplant center, it might be good for them to nevertheless be submitted to a regional match…

Pair 1

Pair 2 Pair 3

Pair 4

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Kidney overview• For kidney exchange, the big problem initially has

been establishing a thick market, and we’ve been trying to do this while solving the new problems concerning congestion and incentives that arise.

• Some of these congestion problems involved the logistics of surgery on the one hand, and the finding of ways to reach the efficient frontier without straining these logistics too much.

• The initial strategic (incentive and equilibrium) considerations we focused on involved individual surgeons and their patients; now we are seeing issues involving transplant centers as the players.

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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.

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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

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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

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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?

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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

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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

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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.

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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.

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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

Stability is an important criterion for a successful clearinghouse.

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GS Deferred Acceptance Algorithm, with men proposing

• 0. If some preferences are not strict, arbitrarily break ties • 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.

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GS’s 2 Remarkable Theorems

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

• Theorem 2 (GS): When all men and women have strict preferences, there always exists an M-optimal stable matching (that every man likes at least as well as any other stable matching), and a W-optimal stable matching. Furthermore, the matching M produced by the deferred acceptance algorithm with men proposing is the M-optimal stable matching. The W-optimal stable matching is the matching W produced by the algorithm when the women propose.

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Incentives—Many to one matching• The 1952 NIMP algorithm is equivalent to the

hospital-proposing deferred acceptance algorithm, i.e. it produces the hospital-optimal stable matching (Roth ’84).

• Many-to-one matching (Roth, 1985) No stable matching mechanism exists that makes it a dominant strategy for all hospitals to state their true preferences, although the student-proposing deferred acceptance algorithm makes it a dominant strategy for all students to state their true preferences.

• Capacity manipulation (Sönmez, 1997) No stable matching mechanism makes it a dominant strategy for a hospital to always reveal its capacity.

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Observation and theory

• Empirical Observation (Roth and Peranson, 1999): The set of stable matchings is small, as is the set of people who can potentially manipulate (about 1 in 1,000).

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Some new theory• Theorem (Immorlica and Mahdian, SODA 2005:) Consider a

marriage model with n men and n women, in which each woman has an arbitrary complete preference list, and each man has a random list of at most k women as his preference list (chosen uniformly and independently). Then, the expected number of women who have more than one stable husband is bounded by a constant that only depends on k (and not on n). (So, as n gets large, the proportion of such women goes to zero…)

• Theorem (Kojima and Pathak, AER forthcoming): In the limit, as n goes to infinity in a regular sequence of random (many-to-one) markets, the proportion of employers who might profit from (any combination of) preference or capacity manipulation goes to zero in the worker proposing deferred acceptance algorithm.

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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…)

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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.