1. Introduction to Market Design, Econ 2056a and Business 4150: Professors Al Roth and Peter Coles, Fall 2008Al RothPeter Coles

2. 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 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 http://kuznets.fas.harvard.edu/~aroth/alroth.html Market design blog: http://marketdesigner.blogspot.com/ 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 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.

4. 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.

5. 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.

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, 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.)

10. 10 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

11. 11 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?

12. 12 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.

13. 13

14. 14 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.

15. 15 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..."

16. 16 Kidney exchange clearinghouse design Roth, 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, forthcoming 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.

17. 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. 17

18. 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,” 18

19. 19 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.

20. 20 Incentives: 2-way exchange involves 4 simultaneous surgeries.

21. 21 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 2Pair 3 Pair 4

22. 22 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.

23. 23 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.

24. 24 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 1995-98Market 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

25. 25 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

26. 26 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?

27. 27 Gale, David and Lloyd Shapley [1962], Two- Sided Matching Model Men = {m 1,..., m n }Women = {w 1,..., w p } PREFERENCES (complete and transitive): – P(mi) = w 3, w 2,... m i...[w 3 > mi w 2 ] – P(wj) = m2, m4,... wj... 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

28. 28 Gale, David and Lloyd Shapley [1962], Two- Sided Matching Model Men = {m 1,..., m n }Women = {w 1,..., w p } PREFERENCES (complete and transitive): – P(mi) = w 3, w 2,... m i...[w 3 > mi w 2 ] – P(wj) = m2, m4,... wj... 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

29. 29 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.

30. 30 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.

31. 31 MarketStableStill in use (halted unraveling) NRMP yesyes (new design in ’98) Edinburgh ('69)yesyes Cardiffyesyes Birminghamnono Edinburgh ('67)nono Newcastlenono Sheffieldnono Cambridgenoyes London Hospitalnoyes Medical Specialtiesyesyes (~30 markets, 1 failure ) Canadian Lawyersyesyes (Alberta, no BC, Ontario) Dental Residenciesyes yes (5 ) (no 2) Osteopaths (< '94)nono Osteopaths (> '94)yes yes Pharmacistsyes yes Reform rabbisyes (first used in ‘97-98)yes Clinical psychyes (first used in ‘99)yes Lab experimentsyesyes. (Kagel&Roth QJE 2000)nono Stability is an important criterion for a successful clearinghouse.

32. 32 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.

33. 33 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.

34. 34 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.

35. 35 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).

36. 36 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.

37. 37 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…)

38. 38 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)

39. Market Design Manifesto We need to understand how markets work well enough to fix them when they’re broken.