Transcript Introduction to Market Design, ECON 285 – 01 Autumn Quarter 2012 Professors Muriel Niederle and Al Roth.

Introduction to Market Design,
ECON 285 – 01
Autumn Quarter 2012
Professors 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.
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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/
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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
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Recommended text (for the early part
of the class)
• Roth, Alvin E. and Marilda Sotomayor TwoSided 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?
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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.
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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.
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• 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
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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 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.
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• 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).
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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
• (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
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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
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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”.
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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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Let’s start with medical labor markets
• They use money (doctors are paid), but they
are prototypical matching markets…
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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:
UNRAVELING
Offers are early, dispersed in
time,
exploding…no
thick
market
Stage 2: UNIFORM DATES
ENFORCED
Deadlines, 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 ...
– P(wj) = m2, m4, ... wj ...
[w3 >mi w2]
Outcomes= matchings: :MW MW
– 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 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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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.
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Example
M = {m1, m2, m3},
W = {w1, w2, w3}
P(m1) = w2,w1,w3
P(m2) = w1,w2,w3
P(m3) = w1,w2,w3
P(w1) = m1,m2,m3
P(w2) = m3,m1,m2
P(w3) = m1,m2,m3
M = ([m1,w1], [m2,w3], [m3,w2]) = W
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GS’s Remarkable Theorem (1st of 2)
• Theorem 1 (GS): A stable matching exists for every
marriage market.
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Another kind of matching algorithm: Priority matching
•
•
•
•
Edinburgh, 1967
Birmingham 1966, 1971, 1978
Newcastle 1970's
Sheffield 196x
No longer in use
"
"
" "
"
"
" "
"
"
" "
In a priority matching algorithm, a 'priority' is defined for each firmworker 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?
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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.
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Market
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Stable
NRMP
yes
Edinburgh ('69)
yes
Cardiff
yes
Birmingham
no
Edinburgh ('67)
no
Newcastle
no
Sheffield
no
Cambridge
no
London Hospital
no
Medical Specialties
yes
Canadian Lawyers
yes
Dental Residencies
yes
Osteopaths (< '94)
no
Osteopaths (> '94)
yes
Pharmacists
yes
Reform rabbis
yes (first used in ‘97-98)
Clinical psych
yes (first used in ‘99)
Still in use (halted unraveling)
yes (new design in ’98)
yes
yes
no
no
no
no
yes
yes
yes (~30 markets, 1 failure)
yes (Alberta, no BC, Ontario)
yes (5 ) (no 2)
no
yes
yes
yes
yes
Stability looks like an important criterion for a successful clearinghouse.
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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…
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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.
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Average Cost of Early Markets
10
Markets with a Clearinghouse
Decentralized Markets
Cost (Dollars)
8
Stable
(Deferred
Acceptance)
algorithm
6
New castle
Priority
algorithm
4
2
0
1-5
6-10
11-15
Markets #
16-20
21-25
30
Offers and acceptances
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Market
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Stable
NRMP
yes
Edinburgh ('69)
yes
Cardiff
yes
Birmingham
no
Edinburgh ('67) no
Newcastle
no
Sheffield
no
Cambridge
no
London Hospital
no
Medical Specialties
yes
Canadian Lawyersyes
Dental Residencies
yes
Osteopaths (< '94)
no
Osteopaths (> '94)
yes
Pharmacists
yes
Reform rabbis
yes (first used in ‘97-98)
Clinical psych
yes (first used in ‘99)
• Lab experiments
(Kagel&Roth QJE 2000)
yes
no
Still in use (halted unraveling)
yes (new design in ’98)
yes
yes
no
no
no
no
yes
yes
yes (~30 markets, 1 failure)
yes (Alberta, no BC, Ontario)
yes (5 ) (no 2)
no
yes
yes
yes
yes
yes.
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…
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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)
•
•
•
•
•
•
Hematology (2006)
Hematology/Oncology (2006)
Infectious Disease (1986-1990; rejoined in 1994)
Oncology (2006)
Pulmonary and Critical Medicine (1986)
Rheumatology (2005)
Primary Care Sports Medicine (1994)
Radiology
•
•
•
Interventional Radiology (2002)
Neuroradiology (2001)
Pediatric Radiology (2003)
Surgical Critical Care (2004)
Thoracic Surgery (1988)
Vascular Surgery (1988)
• Gastroenterology (1986-1999; rejoined Postdoctoral Dental Residencies in the United States
in 2006)
•
Oral and Maxillofacial Surgery (1985)
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)
•
•
•
•
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 they’re broken.
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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…)
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Syllabus Econ 285, Market Design, Niederle and Roth, Autumn
2012 (subject to revision, this version 9/25/12:)
1.
24 Sept: Introduction to market design
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
No class 26 Sept (Yom Kippor)
1 October: Theory of Stable matchings 1
3 October: Theory of Stable matchings 2
8 October: NRMP design, couples,
10 October: congestion and Signaling (APPIC and AEA)
15 October: Generalized matching (Hatfield and Ostrovsky?)
17 October: Kidney exchange 1
22 October: Kidney exchange 2
24 October: Unraveling and gastro 1
29 October: Unraveling 2
31 October School choice
5 November School choice 2
7 November: School choice, Guillaume Haeringer
12 November Schools and slots: Scott Kominers
14 November: Random assignment mechanisms
26 November: ?Rank efficiency (Clayton?)
28 November: Another visitor (Nikhil?)
3 December: Student presentations
5 December: Student presentations
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Matching is important
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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, 1939
Chapter 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].’
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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.
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.
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