1. introduction to market design.2011

8/10/2019 1. Introduction to Market Design.2011

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

Professors Al Rothand Peter Coles,

Fall 2011

[email protected], [email protected]

TF: Assaf Romm: [email protected]
http://kuznets.fas.harvard.edu/~aroth/alroth.htmlhttp://pine.hbs.edu/external/facPersonalShow.do?pid=337272mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://pine.hbs.edu/external/facPersonalShow.do?pid=337272http://kuznets.fas.harvard.edu/~aroth/alroth.html


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Some useful websites

Course web page: for syllabus, including links toreading, and for weekly handouts (includingthese slides):

Economics 2056a : Market Designhttp://isites.harvard.edu/icb/icb.do?keyword=k80599

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

Market design blog:http://marketdesigner.blogspot.com/
http://isites.harvard.edu/icb/icb.do?keyword=k80599http://kuznets.fas.harvard.edu/~aroth/alroth.htmlhttp://marketdesigner.blogspot.com/http://marketdesigner.blogspot.com/http://kuznets.fas.harvard.edu/~aroth/alroth.htmlhttp://isites.harvard.edu/icb/icb.do?keyword=k80599


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

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

explorations of mathematical models, some have been fullof institutional description

Well 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. From time to time well also pose exercises


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Recommended texts Roth, Alvin E. and Marilda Sotomayor Two-Sided

Matching: A Study in Game-Theoretic Modeling andAnalysis, Econometric Society Monograph Series,Cambridge University Press, 1990. (get the paperbackedition.)

Milgrom, Paul "Putting Auction Theory to Work" byPaul Milgrom (Churchill Lectures), CambridgeUniversity Press, 2004

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


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Occasional lunches

After about half the class sessions (judgingfrom past experience), Peter and I willannounce that we are free for lunch

afterwards with anyone interested.

In past years weve normally walked over to

Finale in the Holyoke Center


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Lightning overview of the course

Designis both a verb and a noun, and wellapproach market design both as an activity andas an aspect of markets that we study.

The course will have both substantive andmethodological themes.

Design also comes with a responsibility for detail.Designers cant be satisfied with simple modelsthat explain the general principles underlying amarket; they have to be able to make sure that all

the detailed parts function together.


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Methodology

Responsibility for detail requires the ability todeal with complex institutional features that maybe omitted from simple models.

Game theory, the part of economics that studiesthe rules of the game, provides a frameworkwith which design issues can be addressed.

But dealing with complexity will require newtools, to supplement the analytical toolbox of thetraditional theorist.


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Game Theory, experimentation, and

computation, together with careful observation

of historical and contemporary markets (withparticular attention to the market rules), arecomplementary tools of Design Economics

Computation helps us find answers that arebeyond 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


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An analogy Consider the design of suspension bridges. Their simple

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

But bridge design also concerns metal fatigue, soilmechanics, and the sideways forces of waves and wind.

Many questions concerning these complications cant beanswered analytically, but must be explored using physicalor computational models.

These complications, and how they interact with that part

of the physics captured by the simple model, are theconcern of the engineering literature. Some of this is lesselegant than the simple model, but it allows bridgesdesigned on the same basic model to be built longer andstronger over time, as the complexities and how to dealwith them become better understood.


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

and of auctions.

In recent years there have been some great advances in thetheory of each of these, that brings them much closertogether.

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

(Paul Milgrom and his colleagues, and former students inthis class, have led the way on much of the recenttheoretical work.)


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Substantive lessons from market failuresand successes

To achieve efficient outcomes, marketplaces need makemarkets 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 (2010??) Repugnant: monetary markets

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)

Denverpresently underway (DC, Chicago and/or NewOrleans maybe soon)

American market for new economists Scramble ((thickness) March 2006 Signaling (congestion) December 2007


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Kidney exchange--background There are 89,603patients on the waiting list for

cadaver kidneys in the U.S. (as of 9/1/11) In 2010 34,418 patients were added to the waiting list,

and 27,775 patients were removed from the list. In 2010 there were 10,622 transplants of cadaver

kidneys performed in the U.S.

In the same year, 4,652 patients died while on thewaiting list (and more than 2,110 others were removedfrom the list as Too Sick to Transplant.

In 2010 there were also 6,276 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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4

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.

A l i i bl


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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 personswhose disposable possessions mutually suit each other'swants. There may be many people wanting, and manypossessing those things wanted; but to allow of an act ofbarter, there must be a double coincidence, which willrarely happen. ... the owner of a house may find itunsuitable, and may have his eye upon another houseexactly fitted to his needs. But even if the owner of thissecond house wishes to part with it at all, it is exceedinglyunlikely that he will exactly reciprocate the feelings of thefirst owner, and wish to barter houses. Sellers and

purchasers can only be made to fit by the use of somecommodity... which all are willing to receive for a time, sothat what is obtained by sale in one case, may be used inpurchase in another. This common commodity is called amedium, of exchange..."


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Kidney exchange clearinghouse design

Roth, Alvin E., Tayfun Snmez, and M. Utku nver, KidneyExchange,Quarterly Journal of Economics, 119, 2, May,

2004, 457-488.________started talking to docs________

____ Pairwise Kidney Exchange,Journal of EconomicTheory, 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

Markets with Compatibility-Based Preferences,AmericanEconomic Review, June 2007, 97, 3, June 2007, 828-851

___multi-hospital exchanges become commonhospitalsbecome players in a new kidney game________Ashlagi, Itai and Alvin E. Roth Individual rationality and

participation in large scale, multi-hospital kidneyexchange, working paper, January 2011.


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And in the medical literature

Saidman, SusanL., Alvin E. Roth, Tayfun Snmez, M. Utku nver, 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 Snmez, M. Utku nver, Francis L. Delmonico, and SusanL. Saidman, Utilizing List Exchange and Undirected Donation throughChainPaired 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 nver, and Robert A.Montgomery, A Non-Simultaneous Extended Altruistic Donor Chain, New

England Journal of Medicine , 360;11, March 12, 2009, 1096-1101.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

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http://kuznets.fas.harvard.edu/~aroth/papers/Rees%20etal%20NEJM%202009.pdfhttp://kuznets.fas.harvard.edu/~aroth/papers/Rees%20etal%20NEJM%202009.pdfhttp://kuznets.fas.harvard.edu/~aroth/papers/Rees%20etal%20NEJM%202009.pdfhttp://kuznets.fas.harvard.edu/~aroth/papers/Rees%20etal%20NEJM%202009.pdf


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Theres also a growing CS literature Abraham, D., Blum, A., and Sandholm, T. 2007. Clearing

Algorithms for Barter Exchange Markets: Enabling NationwideKidney Exchanges. In Proceedings of theACM Conference onElectronic Commerce (EC).

Ashlagi, Itai, Felix Fischer, Ian A. Kash, Ariel D. Procaccia,2010,Mix and Match, EC10, June 711, 2010, Cambridge, MA.

Ashlagi, Itai, and Alvin E. Roth 2011 Participation (versus free

riding) in large scale, multi-hospital kidney exchange

Biro, Peter, and Katarina Cechlarova (2007), Inapproximabilityof the kidney exchange problem, Information ProcessingLetters, 101, 5, 16 March 2007, 199-202

Ioannis Caragiannis, Aris Filos-Ratsikas, and Ariel D. Procaccia.An Improved 2-Agent Kidney Exchange Mechanism, July 2011.

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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 (pilot now scheduled for Sept 2010)

Find efficient feasible matchings, in an incentivecompatible way (i.e. in a way that makes it safe foreveryone to reveal their private information and goahead with the resulting exchanges).

Prime incentive issues: All transplants in an exchange performed simultaneously

transplant centers that can do a local exchange shouldnevertheless submit pairs to the regional/national exchange.


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Incentives: 2-way exchange involves 4simultaneoussurgeries.


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The exchange P1-P2results in twotransplantations, but theexchanges P1-P4 and P2-P3results in four.

So even if Pairs 1 and 2 are at the same transplant center, it mightbe 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 weve beentrying to do this while solving the new problemsconcerning congestion and incentives that arise.

Some of these congestion problems involved thelogistics of surgery on the one hand, and the findingof ways to reach the efficient frontier withoutstraining these logistics too much.

The initial strategic (incentive and equilibrium)considerations we focused on involved individual

surgeons and their patients; now we are seeingissues involving transplant centers as the players. (Were scheduled to talk about kidney exchange and

related matters in detail late in the semester.)


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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 41couples, 1,500 positions in 2005)

The redesign in 2005 of the fellowship market

for Gastroenterologists Contemporary issues in labor markets for

Orthopaedic surgeons, neuropsychologists, andlaw clerks for appellate judges.


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Background to redesign of the medicalclearinghouses

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 numberof MARRIED COUPLES

1995-98 Market experienced a crisis of confidence with fearsof substantial decline in orderly participation;

Design effort commissionedto design and compare alternativematching 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: UNRAVELING

Offers are early, dispersed intime, explodingno thick

market

Stage 2: UNIFORM DATES

ENFORCED

Deadlines, congestion

Stage 3:

CENTRALIZED MARKET

CLEARING PROCEDURES


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What makes a clearinghouse successful orunsuccessful?

A matching is stable if there arent a doctor and

residency program, not matched to each other, whowould both prefer to be.

Hypothesis: successful clearinghouses produce stablematchings.

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: :MWMW

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: :MWMW

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 matchings

A matching is

BLOCKED BY AN INDIVIDUAL k if k prefers being single to beingmatched with (k), i.e. k >k(k)

((k) is unacceptable).

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

w >m(m) and m >w(w)

A matching is STABLEif 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 equalsthe core.


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Stable matchings

A matching is

BLOCKED BY AN INDIVIDUAL k if k prefers being single to beingmatched with (k), i.e. k >k(k)

((k) is unacceptable).

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

w >m(m) and m >w(w)

A matching is STABLEif 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 equalsthe 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 QJE2000) 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" themost preferred and rejects all others.

k a. Any man rejected at step k-1 makes a new proposal to itsmost preferred acceptable mate who hasnt yet rejected him.(If no acceptable choices remain, he makes no proposal.)

b. Each woman holds her most preferred acceptable offer todate, and rejects the rest.

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


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GSs 2 Remarkable Theorems

Theorem 1 (GS): A stable matching exists for everymarriage market.

Theorem 2 (GS): When all men and women havestrict preferences, there always exists an M-optimalstable matching (that every man likes at least as wellas any other stable matching), and a W-optimalstable matching. Furthermore, the matching Mproduced by the deferred acceptance algorithm with

men proposing is the M-optimal stable matching.The W-optimal stable matching is the matching Wproduced by the algorithm when the womenpropose.


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IncentivesMany to one matching

The 1952 NIMP algorithmis equivalent to thehospital-proposing deferred acceptance algorithm,

i.e. it produces the hospital-optimal stable matching(Roth 84). (see todays homework for a relatedproblem

Many-to-one matching(Roth, 1985) No stable

matching mechanism exists that makes it adominant strategy for all hospitals to state theirtrue preferences, although the student-proposingdeferred acceptance algorithm makes it a dominantstrategy for all students to state their true

preferences. Capacity manipulation(Snmez, 1997) No stable

matching mechanism makes it a dominant strategyfor 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 ofpeople 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 modelwith n men and n women, in which eachwoman has an arbitrarycomplete preference list, and eachman has a random list of at most k women as his preferencelist (chosen uniformly and independently). Then, the expected

number of women who have more than one stable husband isbounded by a constant that only depends on k (and not on n).(So, as n gets large, the proportion of such women goes tozero)

Theorem (Kojima and Pathak, AER 2009): In the limit, as n

goes to infinity in a regular sequence of random (many-to-one) markets, the proportion of employers who might profitfrom (any combination of) preference or capacitymanipulation goes to zero in the worker proposing deferredacceptance algorithm.

C t NRMP t h


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Current NRMP match(Roth/Peranson algorithm)

Produces student optimal stable matching (asclose 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 instabilitieswith 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)

Stable Clearinghouses (those now using the Roth Peranson Algorithm)


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StableClearinghouses (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; rejoinedin 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)


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Market Design Manifesto

We need to understand how

markets work well enough to fix

them when theyre broken.

H k i


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

of Podiatric Medicinehttp://www.casprcrip.org/html/casprcrip/students.asp

They run a match, and here is the description of theiralgorithm:http://www.casprcrip.org/html/casprcrip/pdf/MatchExpl.pdf(this is also on the class web page)

Is their algorithm equivalent to the hospital proposingdeferred 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 nextweeks 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 problemyou may want tolook ahead in the notes)
http://www.casprcrip.org/html/casprcrip/students.asphttp://www.casprcrip.org/html/casprcrip/students.asphttp://www.casprcrip.org/html/casprcrip/pdf/MatchExpl.pdfhttp://www.casprcrip.org/html/casprcrip/pdf/MatchExpl.pdfhttp://www.casprcrip.org/html/casprcrip/pdf/MatchExpl.pdfhttp://www.casprcrip.org/html/casprcrip/students.asp

1. introduction to market design.2011

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