A supply and demand model for stable matchings, by Eduardo Azevedo and Jacob Leshno

Much of two-sided matching theory has been developed using discrete mathematics, which has led to beautiful theorems about lattices and stable matchings that are optimal for one side of the market or the other. Since the agents on each side of the market can be quite heterogeneous (which is why who is matched to whom is important), there is a lot of information in each stable matching, which can therefore be hard to summarize succinctly.

Now Eduardo Azevedo and Jacob Leshno have a very nice model of two sided matching in which one side of the market is a continuum, or can be approximated as such via a converging sequence of finite markets, while the other side is finite. Think college admissions, with lots of students and a finite set of colleges. In their model, there is a (generically) unique stable matching, and it can be characterized by a low dimensional set of price-like scalar thresholds, one for each college.

Modeling a continuum of students means that students have to be characterized in some sense, and they find a simple, general way to do this, that works well in the finite case also. A student is characterized by an arbitrary preference over colleges (there are only finitely many of these, since there's a fixed finite set of colleges) and a vector of scores, one for each college, which characterizes each college's preferences over students (each college ranks students in their order on the college's own score). They show that a stable matching becomes a very simple object--it is the solution to a set of supply and demand equations, in which each college is characterized by a threshold, and students are admitted to their most preferred college among those that score them above that college's threshold.

This simple characterization of stability considerably simplifies the investigation of comparative statics.They illustrate this with a price-theoretic analysis of how competition induces schools to improve quality, and why this may not benefit some types of student.

It looks like this will be quite a useful model.

Here's the paper and abstract:

A Supply and Demand Framework for Two-Sided Matching Markets by EDUARDO M. AZEVEDO AND JACOB D. LESHNO

Abstract: "We propose a new model of two-sided matching markets, which allows for complex heterogeneous preferences, but is more tractable than the standard model, yielding rich comparative statics and new results on large matching markets.


"We simplify the standard Gale and Shapley (1962) model in two ways. First, following Aumann (1962) we consider a setting where a finite number of agents on one side (colleges or firms) are matched to a continuum mass of agents on the other side (students or workers). Second, we show that, in both the discrete and continuum model, stable matchings have a very simple structure, with colleges accepting students ranked above a threshold, and students demanding their favorite college that will accept them. Moreover, stable matchings may be found by solving for thresholds that balance supply and demand for colleges. We give general conditions under which the continuum model admits a unique stable matching, in contrast to the standard discrete model. This stable matching varies continuously with the parameters of the model, and comparative statics may be derived as in competitive equilibrium theory, through the market clearing equations. Moreover, given a sequence of large discrete economies converging to a limit economy, the set of stable matchings of the discrete economies converges to the stable matching of the limit economy.


"We bound the rate of convergence of the set of stable matchings of large discrete economies to the continuum approximation, and show that comparative statics regarding the unique stable matching of the continuum model extend to strong set ordering of the sets of stable matchings of approximating discrete economies. We model the transferrable utility case, as in Becker (1973). We characterize the limit of school choice mechanisms used in practice, generalizing previous results of Che and Kojima (2010). Finally, we illustrate the model's applicability by quantifying how competition induced by school choice gives schools incentives to invest in quality. Specifically, we show that schools have muted, and possibly even negative incentives to invest in quality dimensions that benefit lower ranked students."

As I've mentioned in previous blog posts about some of their other papers (here about Eduardo and here about Jacob), they are both on the job market this year. Here are their other papers (Eduardo's; Jacob's). You could hire them both:)

For Love or Money

Kim Krawiec writes
"The conference volume For Love Or Money: Defining Relationships in Law and Life has finally been published, yeah!  The introduction is here.  My three posts, done just before and after the conference and discussing the event are here, here, and here.  The table of contents is [here]."

Here are the posts on my blog that come up when I search for "Krawiec".

Market design at INFORMS, Nov 13-15 in Charlotte NC

When I got my Ph.D. in Operations Research in 1974, it looked like game theory might find a natural home in OR and Management Science. Shortly after, the new journal MOR was formed, with Bob Aumann as the area editor for game theory.  But...things didn't turn out that way, and game theory caught on in Economics much more than in OR. And game theory eventually gave birth to the emerging field of market design.

It looks like market design may be a theme that brings game theory back into OR/MS. Here are some sessions to be presented at the forthcoming INFORMS meetings...

https://informs.emeetingsonline.com/emeetings/formbuilder/clustersessionlist.asp?clnno=2672&mmnno=206

Cluster Information

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Title: AuctionsChair: Bob Day,Assistant Professor, University of Connecticut, 2100 Hillside Rd, Unit 1041, Storrs CT 06269-1041, United States of America, bob.day@business.uconn.edu
Co-Chair: Martin Bichler,TU Munich, Boltzmannstr. 3, Garching 85748, Germany, bichler@in.tum.de

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Sunday Nov 13, 08:00 - 09:30 : Combinatorial Auction Design and Applications IChair: Dries Goossens,K.U.Leuven, Naamsestraat 69, Leuven 3000, Belgium, Dries.Goossens@econ.kuleuven.be
Sunday Nov 13, 11:00 - 12:30 : Core-Selecting AuctionsChair: Bob Day,Assistant Professor, University of Connecticut, 2100 Hillside Rd, Unit 1041, Storrs CT 06269-1041, United States of America, bob.day@business.uconn.edu
Sunday Nov 13, 13:30 - 15:00 : Spectrum AuctionsChair: Bob Day,Assistant Professor, University of Connecticut, 2100 Hillside Rd, Unit 1041, Storrs CT 06269-1041, United States of America, bob.day@business.uconn.edu
Sunday Nov 13, 16:30 - 18:00 : Panel on Research Challenges in Market DesignChair: Martin Bichler,TU Munich, Boltzmannstr. 3, Garching 85748, Germany, bichler@in.tum.de
Monday Nov 14, 08:00 - 09:30 : Combinatorial Auction Design and Applications IIChair: Benjamin Lubin,Assistant Professor, Boston University, 595 Commonwealth Ave, Information Systems Department, Boston MA 02215, United States of America, blubin@bu.edu
Monday Nov 14, 11:00 - 12:30 : Procurement Auctions and Combinatorial ExchangesChair: Damian Beil,Associate Professor, University of Michigan, 701 Tappan St, Ann Arbor MI 48109, United States of America, dbeil@umich.edu
Monday Nov 14, 13:30 - 15:00 : Algorithmic Game TheoryChair: Kevin Leyton-Brown,University of British Columbia, 201-2366 Main Mall, Vancouver BC, Canada, kevinlb@cs.ubc.ca
Monday Nov 14, 16:30 - 18:00 : Behavioral Market DesignChair: Kemal Guler,HP Labs, 1501 Page Mill Rd MS 1040, Palo Alto CA, United States of America, kemal.guler@hp.com
Tuesday Nov 15, 08:00 - 09:30 : Auctions and Trading AgentsChair: Wolf Ketter,Assistant Professor, Rotterdam School of Management, Burgemeester Oudlaan 50, T9-07, Rotterdam 3062PA, Netherlands, WKetter@rsm.nl
Tuesday Nov 15, 11:00 - 12:30 : Algorithmic and Implementation Issues in AuctionsChair: Sasa Pekec,Duke University, Fuqua School of Business, Durham NC, United States of America, pekec@duke.edu
Tuesday Nov 15, 13:30 - 15:00 : Auctions and their ApplicationsChair: Ravi Bapna,Professor, University of Minnesota, 4600 Washburn Avenue South, Minneapolis MN 55410, United States of America, rbapna@umn.edu
Tuesday Nov 15, 16:30 - 18:00 : Auction Design with Multi-dimensional TypesChair: Sasa Pekec,Duke University, Fuqua School of Business, Durham NC, United States of America, pekec@duke.edu

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How to allocate goods when the waiting list is essentially infinite. New queues for overloaded systems, by Jacob Leshno

Matching is about who gets what when allocation isn't entirely by price. And a common means of allocating scarce goods is by waiting lists. But there are special problems to consider when the goods being allocated are so scarce that most of those waiting will never receive an allocation. How should applicants be matched to goods when they become available, and how can applicants be given an incentive to pass on goods that might more efficiently be allocated to someone else, if match quality is private information? In considering these things, Jacob Leshno opens up a new front for market design, and introduces a novel kind of queue and some new ideas to the venerable study of queues.

For example, the city of Chicago caps the waiting list for public housing at 60,000 people. The total supply of public housing that they administer is around 20,000 units, and units only become vacant after being occupied for several years, so it's clear that most people who are eligible for public housing will never get it; the system is simply overloaded.  How should the places be allocated? The whole point of public housing is that we don't want to use price to determine who gets what by pricing the poorest out of the market.

Dynamic Matching in Overloaded Systems by Jacob Leshno
Abstract: "In many assignment problems items arrive stochastically over time. When items are scarce agents form an overloaded waiting list and items are dynamically allocated as they arrive; two examples are public housing and organs for transplant. Even when all the scarce items are allocated, there is the efficiency question of how to assign the right items to the right agents. I develop a model in which impatient agents with heterogeneous preferences wait to be assigned scarce heterogeneous items that arrive stochastically over time. Social welfare is maximized by appropriately matching agents to items, but an individual impatient agent may misreport her preferences to receive an earlier mismatched item. To incentivize an agent to avoid mismatch, the policy needs to provide the agent with a (stochastic) guarantee of future assignment, which I model as putting the agents in a priority buffer-queue. I first consider a standard queue-based allocation policy and derive its welfare properties. To determine the optimal policy, I formulate the dynamic assignment problem as a dynamic mechanism design problem without transfers. The resulting optimal incentive compatible policy uses a buffer-queue of a new queueing policy, the uniform wait queue, to minimize the probability of mismatching agents. Finally, I derive a robustly optimal policy which uses a simple rule: giving equal priority to every agent who declines a mismatched item (a SIRO buffer-queue). This robustly optimal policy has several good properties that make it a compelling market design policy recommendation."

That is, to reduce mismatches, the allocation process has to give some people the incentive to wait when they are offered a space of the “wrong” type for them, e.g. in a wrong location.  It is easy to incentivize the first such person, e.g. you could promise him that if he declines the space currently being offered, he will be the first to get a space in his preferred location when it becomes available. If the anticipated wait is short enough, this could be an attractive proposition. But suppose the next person on line likes the same location as the first person? You couldn’t offer him as good a deal, since he would now have to wait for the second space to become available in his preferred location. So, it could be that, before someone who actually prefers the current location comes to the head of the line (which they have to reveal, since it’s private information), a mismatch would occur when a person decides it’s better to take the wrong location than to wait further for the kth place at the location he prefers. In a simple model with just two locations, Jacob shows (the far from obvious conclusion) that maximizing the number k of people willing to wait for their preferred location is the same as minimizing the steady state probability of mismatches.

But conventional queue disciplines (e.g. FIFO, LIFO, etc.) don’t maximize the number of people willing to wait in this buffer queue of folks who would have been mismatched if they had taken what was first offered to them. In solving the optimization problem, Jacob discovered/invented a new queue discipline that he calls uniform wait. People who choose to wait in the buffer queue for a given location are given different probabilities of being called to the head of the queue as different housing spaces arrive to be allocated, based on how many people have joined the buffer queue so far, so that the expected wait for any of the 1,…k people who might decide to wait is equal at the moment that they have to decide whether to join the buffer queue. That is, if you are the first to join, you will get the location you are waiting for if it arrives before someone else has joined, and after that you will have some probability of getting each apartment-at-the-right-location as one arrives, and that probability will depend on how many other people are also waiting. In this way, the 2^nd through kth people who join can also be given good incentives to wait for a perfect match; they might not have to wait for all the people ahead of them to be served. Everyone faces the same choice; to take the offered apartment (at the wrong location) or to have a fixed (uniform) waiting time for one at the location they prefer, whether they would be the first person in the buffer queue or the kth. Mismatches will now occur only when this buffer queue has so many people that new people prefer to accept a mismatch than to wait.

Jacob also proposes an almost optimal, more robust solution (that doesn't have to be tuned to the particular parameters of the problem) which is to place mismatched applicants into an unordered buffer, from which they are selected at random when an object of the kind they are all waiting for becomes available.

Incidentally, Jacob is a local hero:
"The Martin Award is awarded to HBS doctoral students enrolled in the PhD in Business Economics program who have excelled at conducting outstanding academic research. This year, the faculty have selected one student to receive the Martin Award.
Jacob Leshno – Jacob studies market design, specifically the dynamic allocation of scarce resources through the use of waiting lists."

Jacob is on the job market this year, you could hire him. Here's a link to his papers.

Should you guess on the SAT? And do you? Katie Baldiga finds men and women are different.

What accounts for the gender gap in (high) test scores, for the fact that SAT scores predict college success less well for women then for men, and perhaps for other gaps that persist between men and women?  An innovative line of inquiry is carried out in a paper whose title telegraphs what may be part of the answer:
Gender Differences in Willingness to Guess and the Implications for Test Scores by Katherine Baldiga

Here's the Abstract:  "Multiple-choice tests play a large role in determining academic and professional outcomes. Performance on these tests hinges not only on a test-taker's knowledge of the material but also on his willingness to guess when unsure about the answer. In this paper, we present the results of an experiment that explores whether women skip more questions than men. The experimental test consists of practice questions from the World History and U.S. History SAT II subject tests; we vary the size of the penalty imposed for a wrong answer and the salience of the evaluative nature of the task. We find that when no penalty is assessed for a wrong answer, all test-takers answer every question. But, when there is a small penalty for wrong answers and the task is explicitly framed as an SAT, women answer signifi cantly fewer questions than men. We see no differences in knowledge of the material or confidence in these test-takers, and differences in risk preferences fail to explain all of the observed gap. Because the gender gap exists only when the task is framed as an SAT, we argue that differences in competitive attitudes may drive the gender differences we observe. Finally, we show that, conditional on their knowledge of the material, test-takers who skip questions do significantly worse on our experimental test, putting women and more risk averse test-takers at a disadvantage."

Katie's experiment is designed as follows. Each subject participates in only one of four experimental conditions, determined by whether there is a penalty for answering incorrectly or not (i.e. whether points are subtracted for wrong answers or not), and whether or not the test is framed as an SAT, by reminding participants that the questions are drawn from SATs and will be scored like SATs. That's the "between subject" part of her design, and the abstract makes clear how those comparisons played out.

The "within subject" part of the design is that every subject participated in three tests. The first consisted of the SAT questions, and subjects were free to skip questions they did not feel confident they could answer. The second was a test of risk aversion. The third test consisted of the same SAT questions as the first, but subjects were asked to answer every question even if they were not confident that they knew the answer. Having the data from the three tests for each subject allows Katie to compare, on the first test, subjects who did equally well when they answered all questions, and to determine how much of the skipping of questions can be accounted for by differences in their risk aversion. This is what lets her see that the women skipped more questions, and got lower scores than the men, even when they could answer the same number of questions correctly. Which could be one of the reasons why the women's scores would predict future performance less well than the men's.

Katie is a theorist as well as an experimenter: here are her other papers, on social choice theory. She is on the job market this year; you could hire her.

If you are at the ESA meetings in Tucson tomorrow you can also listen to her in what looks to be a great session (I've heard all the speakers before):  Friday, November 11, 1:20 pm – 2:40pm,
Session 4, Ocotillo: GENDER 2

Katherine Baldiga, “Gender Differences in Willingness to Guess”
Johanna Mollerstrom, “Framing and Gender: It's all about the Women”
Muriel Niederle, “Do Single-Sex Schools Make Boys and Girls More Competitive?”

Matching Japanese Doctors: problems with the current mechanisms, and suggestions for improvement by Yuichiro Kamada and Fuhito Kojima

How to get more doctors into rural hospitals? That's a problem that confronts Japanese medical administrators, and American ones too. Apparently the Japanese Ministry of Health, Labor and Welfare has somewhat more control over the medical labor market than is available in the U.S., since they have instituted regional caps on how many new doctors--residents--can be assigned to urban regions.

But the way that they have implemented these caps, and integrated them with the job market for Japanese medical residents, isn't efficient. This is pointed out in a new paper which also proposes and analyzes an alternative design with more appealing properties. (A related paper also considers a simpler fix for the problem, and discusses why this wouldn't quite work...). Here's the new paper:
Improving Efficiency in Matching Markets with Regional Caps: The Case of the Japan Residency Matching Program by Yuichiro Kamada and Fuhito Kojima), December 2010. (Revise and Resubmit, American Economic Review.

(A non-technical introduction to this paper (in Japanese) is here (written by Yuichiro Kamada, Fuhito Kojima and Jun Wako), and here's a short summary in English, which also discusses why a simple fix--an "iterated deferred acceptance algorithm"-- wouldn't be strategy proof for doctors): Stability and Strategy-Proofness for Matching with Constraints: A Problem in the Japanese Medical Matching and Its Solution by Yuichiro Kamada and Fuhito Kojima, September 2011, Forthcoming, American Economic Review Papers and Proceedings.)

Here's the Abstract: "In an attempt to increase the placement of medical residents in rural hospitals, the Japanese government recently introduced "regional caps" which restrict the total number of residents matched within each region of the country. To accommodate regional caps, the government modified the deferred acceptance mechanism in a particular manner. Motivated by this policy change, we study the design of matching markets under constraints on doctor distribution. This paper shows that the Japanese mechanism may result in avoidable inefficiency and instability and proposes a better mechanism that improves upon it in terms of efficiency and stability while respecting the regional caps."

The inefficiency that they observe occurs arises because of the way the regional cap is translated into caps on the number of residents that can be hired by individual hospitals in the region. If the regional cap is to be, say, 75% of the total of the regional hospitals' original capacity to receive new residents in the Japanese Medical Resident Matching Program (JRMP), then each hospital's individual capacity is set to be .75 of its original capacity. The inefficiency arises when some hospitals fail to fill all of their capacity defined in this way, while other hospitals, which have filled their new, artificially low capacity, are prevented from hiring extra residents even though they could do so without violating the cap on the number of residents allowed in the region. These hospitals could even be part of blocking pairs that would not violate the regional caps, i.e.the outcome would be unstable even under an appropriately defined notion of stability with regional caps.

The JRMP uses a doctor-proposing deferred acceptance algorithm (like the U.S. NRMP, although apparently without the many match variations involved in the American match.) One way proposed to fix the problem described above would be to run the deferred acceptance algorithm once, and if some hospitals in a region had empty positions, allow these to revert back to other hospitals in the region and run the JRMP again. Yuichiro and Fuhito observe that this iterated deferred acceptance algorithm wouldn't be strategy-proof for doctors: it might give doctors incentives to truncate the preference lists they submit.

Instead, they observe that each proposed matching determines not only an assignment of residents to hospitals, but also, for each region, a vector of how many residents have been assigned to each of the region's hospitals. If this vector is evaluated according to some "regional preference relation" over vectors that obeys the substitutes property, then a notion of "stability under regional preferences" can be defined that allows many of the recent results from the literature on matching with contracts to be applied. (An example of a regional preference with the substitutes property would be to prefer vectors in which hospitals were closer to having proportional caps to those in which some hospitals received disproportionately more residents than others.)

They propose what they call a (doctor-proposing) Flexible Deferred Acceptance Algorithm, which allows hospitals to more flexibly determine how many residents to hire, while respecting the regional caps. The way it works is that, after a conventional doctor-proposing step of the deferred acceptance algorithm, each region selects its most preferred feasible vector of capacities, and hospitals in each region choose their choice sets with respect to this capacity, and reject only those applicants who aren't chosen under this capacity. It produces an outcome that is both stable under regional preferences and strategy proof for doctors.

It looks like it could be put to use in Japan in the years to come.

Yuichiro is an already-widely published game theorist with broad interests, mostly in more classical kinds of game theory. His papers are here. You could hire him this year.

Market design in a future of trusted smart markets: paper by Eduardo Azevedo and Eric Budish

The recent NBER conference on market design had a number of remarkable papers. One of them, by Eduardo Azevedo and Eric Budish, seems to me to offer a tantalizing glimpse at what market design might look at some time in the not too distant future when there is a high level of trust in computerized "smart" markets in which a proxy agent reliably acts on your behalf.

At least that's one way to interpret their paper "Strategyproofness in the Large as a Desideratum for Market Design." Among other things, it considers a kind of extension of the revelation principle that would allow a non-strategy-proof mechanism with an attractive Bayesian Nash equilibrium to be converted into a direct mechanism (e.g. one in which agents were asked to reveal their preferences) that would be "strategy proof in the large," (SP-L) i.e. approximately strategy proof in large markets, and strategy proof in the limit. (Another big contribution of their paper is making precise the idea of strategy proofness in the large, which, they argue, may be a desirable criterion when no strategy proof mechanism exists, or when markets are large...the idea is that mechanisms are SP-L but not strategy proof when they allow players' reports to influence prices in ways that vanish in the limit, but mechanisms that aren't even SP-L allow more fundamental manipulations, e.g. they don't give you what you want even when you're a price taker.)

About the revelation principle type mechanisms hey say:
"The construction works as follows. Agents report their types to our mechanism. Our mechanism then calculates the empirical distribution of these types, and then “activates” the Bayes-Nash equilibrium strategy of the original mechanism associated with this empirical. If agents all report their preferences truthfully, this construction will yield the same outcome as the original mechanism in the large-market limit, because the empirical distribution of reported types converges to the underlying true distribution. The subtle part of our construction is what happens if some agents systematically misreport their preferences, e.g., they make mistakes. Suppose the true prior is u , but for some reason the agents other than agent i systematically misreport their preferences, according to distribution m. In a finite market, with sampling error, the empirical distribution of the other agents’ reports is say m^ . As the market grows large, m^ is converging to m, and also i’s influence on the empirical distribution is vanishing. Thus in the limit, our construction will activate the Bayes-Nash equilibrium strategy associated with m. This is the “wrong” prior – but agent i does not care. From his perspective, the other agents are reporting according to m, and then playing the Bayes-Nash equilibrium strategy associated with m, so i too wishes to play the Bayes-Nash equilibrium strategy associated with m. This is exactly what our constructed mechanism does on i’s behalf in the limit. Hence, no matter how the other agents play, i wishes to report his own type truthfully in the limit, i.e., the constructed mechanism is SP-L."

The attraction of such a mechanism of course is that it doesn't depend on the agents reaching a Bayes-Nash equilibrium, which is the problem with mechanisms whose desirability is based on the attractiveness of their equilibrium behavior. Equilibrium may be hard to reach, and such mechanisms may perform badly in practice as a result. But coordination on an equilibrium is much easier when truth telling is a dominant strategy.

The reason this seems like a future mechanism rather than one that is promising for practical application right now is that it is pretty opaque, the opposite of transparent. I can't yet imagine going to e.g. a school district and proposing such a mechanism, which you'd have to sell to parents by saying "tell us your true preferences, and we'll act on your behalf to get you your highest ranked school choice by playing the equilibrium that will arise when we see the choices of all families." The problem is not just that the equilibrium might be hard to describe in the abstract, but that this difficulty is compounded by the fact that assignments will depend in this hard to describe way on an unknown distribution of preferences.

But what might be a tough sell today will be a much easier sell when everyone is accustomed to having their data automatically backed up in the cloud by software that optimizes performance based on things only it observes, and to having their electricity consumption mediated by smart meters that run the air-conditioner in a way that reduces costs based on spot prices, etc.

So...engineering is like that. Just as bridges have gotten longer and stronger over time, there's no reason to think that the market designs of today will be the ones we build in the future. The prospect of confidently putting yourself in the hands of a non-transparent automated expert that you may not understand, a "Martian system" so to speak, may be agreeable to the general public of the future.

(The phrase "Martian system" is one I recall from the early days of expert systems and decision aids. The idea was that you were likely to trust an automated adviser more if you could understand its reasoning, and so judge when its advice was likely to be correct. If you got a non-intuitive answer from an opaque oracle, a "martian system" instead of an expert system, you might worry that the answer was wrong because of wrong inputs or bad construction, and so ignore it. But a transparent system might convince you that a non-intuitive answer was correct, if you were more confident that when it wasn't correct you could tell. But if the martian adviser became so reliable that you could be sure he would not produce an incorrect answer, his opacity might become less of a drawback, since you could rely on him anyway.)

By the way, did I mention that Eduardo is on the job market this year? He's a talented theorist with broad interests who has already made important contributions to matching theory, among other things. Here are his papers. You could hire him.

What do policy makers want from a market design? And what would be the consequences of giving it to them? Clayton Featherstone on rank efficiency.

A surprising variety of allocation mechanisms, such as those used for school choice, ask participants to rank-order the alternatives; i.e. to indicate their first choice, second, third, and so forth. Not surprisingly, one thing that policy makers want to know about any proposed mechanism is how many people will receive their first choice, second, third, and so on.

Clayton Featherstone is a market designer who already has an unusual amount of experience in designing and implementing choice mechanisms. (If you recently got an assignment from Teach for America, or were assigned to a country for your global immersion requirement at HBS, you've benefited from his work.) His job market paper is an investigation of the properties of "rank efficient" mechanisms, which are designed to produce outcomes whose distribution of ranks can't be stochastically dominated:
Rank Efficiency: Investigating a Widespread Ordinal Welfare Criterion 

 Here's the Abstract: "Many institutions that allocate scarce goods based on rank-order preferences gauge the success of their assignments by looking at rank distributions, that is, at how many participants get their first choice, how many get their second choice, and so on. For example, San Francisco Unified School District, Teach for America, and Harvard Business School all evaluate assignments in this way. Preferences over rank distributions capture the practical (but non-Paretian) intuition that hurting one agent to help ten might be desirable. Motivated by this, call an assignment rank efficient if its rank distribution cannot feasibly be stochastically dominated. Rank efficient mechanisms are simple linear programs that can be solved either by a computer or through a sequential improvement process where at each step, the policy-maker executes a potentially non-Pareto-improving trade cycle. Both methods are used in the field. Preference data from Featherstone and Roth (2011)'s study of a strategy-proof match shows that if agents were to truthfully reveal their preferences, a rank efficient mechanism could significantly outperform alternatives like random serial dictatorship and the probabilistic serial mechanism. Rank efficiency also dovetails nicely with previous literature: it is a refinement of ordinal efficiency (and hence of ex post efficiency). Although rank efficiency is theoretically incompatible with strategy-proofness, rank efficient mechanisms can admit a truth-telling equilibrium in low information environments. Finally, a competitive equilibrium mechanism like that of Hylland and Zeckhauser (1979) generates a straightforward generalization of rank efficiency and sheds light on how rank efficiency interfaces with fairness considerations."

Clayton’s paper also solves an empirical puzzle about those matching mechanisms that we see “in the wild”. The theory literature has paid a good deal of attention to ordinally efficient mechanisms, as first described by Bogomolnaia and Moulin, who showed that ordinal efficiency can be obtained through a class of “simultaneous eating” mechanisms. But, despite the appeal of ordinal efficiency, no one has ever reported that such mechanisms have been observed in use. Clayton shows that a class of linear programming mechanisms  and an equivalent class of incremental improvement mechanisms that we do observe in practice produce rank efficient outcomes. So, he shows, there are ordinally efficient mechanisms in use; just not those that were previously known to produce ordinally efficient outcomes before he showed that they produced rank efficient outcomes and that rank efficiency implies ordinal efficiency.

Clayton is an unusually experienced market designer whose field experience motivates novel theoretical insights. He's also a talented experimenter who studies market design issues in the lab. He's a Stanford Ph.D. who is finishing up a two-year postdoc with me at Harvard. His other papers are on his Stanford job market page; you could hire him this year.

Five Harvard candidates for the Economics job market this year (2011-12)

One of the pleasures of being a professor of economics is the opportunity to interact closely with young economists just as they metamorphose  from being (merely) wonderful students into economists who teach us important new things.

The Talmud makes the point pretty nicely: "The sages said: I have learned much wisdom from my teacher, more from my colleagues and the most from my students" (BT Ta'anit 7a).

This year has been a crash course for me, since I am helping introduce five exceptional young economists to the job market: one postdoc, two students whose main adviser I was privileged to be, and two students who I helped to advise on papers of mutual interest.

They are Clayton Featherstone (also on the Stanford job market page here);
Eduardo Azevedo, and Jacob Leshno; and Yuichiro Kamada, and Katie Baldiga.

I hope to blog about one or more papers by each of them this week, Monday through Friday, if I can keep up. (I don't promise any particular order, let's see how much I can remember about each of them in time; at least this should help me keep their names straight:)

I'll update this announcement with links to the particular posts (and eventually with job market news), for future reference.

What do policy makers want from a market design? And what would be the consequences of giving it to them? Clayton Featherstone on rank efficiency.

Market design in a future of trusted smart markets: paper by Eduardo Azevedo and Eric Budish

Matching Japanese Doctors: problems with the current mechanisms, and suggestions for improvement by Yuichiro Kamada and Fuhito Kojima

Should you guess on the SAT? And do you? Katie Baldiga finds men and women are different.

How to allocate goods when the waiting list is essentially infinite. New queues for overloaded systems, by Jacob Leshno

A supply and demand model for stable matchings, by Eduardo Azevedo and Jacob Leshno

*******************April 2012 updates****************

Katie Baldiga defends her Ph.D. dissertation 

She and her significant other LC solved the two-body problem this year (!), and will be together at The Ohio State University, which is now more than ever a hotbed of experimental economics.

Yuichiro Kamada defends his Ph.D. dissertation

He will be going next year to a postdoc at Yale, after which he'll take up a position at Berkeley-Haas.

Eduardo Azevedo defends his Ph.D. dissertation

As of April 26 it isn't clear whether he'll be working next year in Philadelphia, NYC, or Chicago, which will depend on his fiance's jobmarket, which is still to be concluded.
Update: May 11--It's Wharton.

Jacob Leshno defends his Ph.D. dissertation

He will be going next year to a postdoc at Microsoft Research in Cambridge, after which he'll take up a position at Columbia GSB.

And Clayton Featherstone, who as a postdoc needed no defense (or maybe was indefensible?) will be going next year to Wharton.

ESA conference in Tucson, November 10-12

Here's the program for the 2011 Regional ESA Conference, November 10-12, 2011.

One striking thing about the program is that there are four sessions of papers focusing on gender.

Colbert on proposal to repeal Florida's dwarf tossing ban

Colbert Supports Repeal Of Dwarf-Tossing Ban Proposed By Florida Legislator Ritch Workman

(Dwarf tossing was one of the repugnant transactions I described in
Roth, Alvin E. "Repugnance as a Constraint on Markets", Journal of Economic Perspectives, 21:3, Summer, 2007, pp. 37-58.)


HT: Parag Pathak

College admissions trends, 2011 edition

NACAC, the National Association for College Admissions Counseling has released a new report:
College Admission Trends for 2011: Uncertain Times Lead Colleges to Lean More Heavily on Wait Lists; Acceptance Rate for Four-Year Colleges Declines Slightly, NACAC Finds

While much of the discussion in the press focuses on the small group of super selective colleges that admit fewer than 10% of applicants, the report indicates that the average admit rate over all four year American colleges and universities is 65%.

Academic publication: design of the market for (scholarly) ideas

Some new additions to the venerable discussion of how to organize academic journals and other outlets for (peer reviewed) ideas.

Noam Nisan reflects on The problem with journals, following a post by Tim Gowers, How might we get to a new model of mathematical publishing?

HT: László Sándor on google+

Science exchange

One of the notable things about this description is the ambivalence about monetary payments...

Online Marketplace Helps Professors Outsource Their Lab Research

Science Exchange

"The site functions like a marketplace, linking researchers who need to outsource parts of their work with people from institutions and companies who can provide that help. The providers bid, the researchers pick the bid that suits them best, and Science Exchange takes about a 5 percent cut (that percentage drops for bids worth more than $5,000).
The idea for the project came from Ms. Iorns’s own problems outsourcing research to other institutions. “The hardest part was paying” for such services, Ms. Iorns said, because universities often don’t have a protocol for how to pay for outsourced research.
This is not the first effort to use the Internet to link researchers to the facilities they need, but the “market aspect” of Science Exchange makes it different, said Edward G. Derrick, chief program director for the Center of Science Policy and Society Programs at the American Association for the Advancement of Science.
The site’s model has raised questions for Michael R. Rossi, director of the Cancer Genomics Shared Resource at Emory University’s Winship Cancer Institute. Mr. Rossi thinks researchers may get into trouble with the National Institutes of Health and other institutions that support them if they pay a third party a fee to find outsourced work. “That really could become a big problem,” Mr. Rossi said.
Ms. Iorns, though, said she has been in contact with the NIH’s National Center for Research Resources, and she said officials there have been enthusiastic about the idea. “This is something they’ve really wanted to set up for some time,” she said."

Movie on Iranian kidney transplant market--bureaucracy, price negotiations, and surgery

Buying and selling kidneys in Iran seems to involve a good deal of bureaucracy and lots of negotiations, followed, in this movie, by two living-donor transplants that seem to have been successful. Both buyers and sellers are poor...
The movie runs about fifty minutes. Here it is: Iranian Kidney Bargain Sale.

And see my earlier post: The market for kidneys in Iran

HT: Federico Echenique

A marketplace for Harvard babysitters

If you work at Harvard, you might be able to hire a Harvard student as a babysitter. Here's the announcement:

Dear Colleague,

I am writing to let you know about an exciting new service available exclusively to the Harvard community: It’s a Harvard PIN-protected babysitting website, called Web Access to Care at Harvard, or the WATCH portal.  Please visit the site at [xxx]

The WATCH portal links Harvard parents – faculty, staff and students – to Harvard students, both undergraduate and graduate, who want to babysit. In addition, Harvard employees are able to sponsor high school and college students who are members of their families to be babysitters.

If you are a parent and think you might need child care in the future, please register with the site and feel free to browse caregiver profiles. If you are actively looking for child care right now, please go ahead and post a job! And if you have high school or college age children interested in babysitting, register them as well.

We’re very excited about this new service and the opportunities it brings to maximize connections within the Harvard community.  

Kidney exchange--gaps in financing

Here's a disturbing editorial from the Globe and Mail, published Oct. 26, 2011. It represents one of the (many) gaps in financing that reflect the growth pangs of kidney exchange. This and other more systematic financial issues need to be resolved if kidney exchange (also called kidney paired donation or, in Canada apparently, kidney swaps) is to stabilize and reach its full potential as a treatment option. In this case an altruistic donor has been left without proper care.

Help the life-giver left with the disfigured body

"Donating a kidney to a stranger is an act of love – and of life. It allows a sick person to become healthy again, and saves the medical system $50,000 a year.

"There is inherent risk in all surgery, but donors assume that, if something goes wrong, the system will take care of them.

"However, that is not what happened to a man from British Columbia who donated his kidney to an anonymous recipient in Toronto in 2009, as part of an innovative new “kidney swap” program. He ended up with a bulge on the left side of his abdomen caused by a pinched nerve during surgery. “Every time I look down, I see this big flap of skin. The nerve that contracts the muscle was cut, which means that the area is flabby and lopsided,” he says. He has tried for two years to get B.C. Health to pay for the surgery to correct his asymmetrical abdomen; the ministry has refused, however, saying the $10,000 operation would be cosmetic. The Ontario hospital where he donated his kidney says it can't help him either."

The roommate problem on TV

James Boudreau writes to alert us to some matching theory on television:

"The NBC show ``Community'' chronicles the misadventures of a diverse and wacky group of students at a community college.  On the last night's episode (season 3, episode three, ``Competitive Ecology'') the group was confronted with the problem of dividing into pairs for the purpose of being lab partners.  When their initial pairings don't work out, one member of the group realizes that they are in a classic roommates problem and suggests that they re-match by writing down lists of ordinal preferences and submitting them to one member of the group who is unanimously selected  as the matchmaker.  Unfortunately, the algorithm that the matchmaker uses (which focuses on balancing popularity across the pairs) proves to be unstable--eventually the group is forced to share one set of equipment since they can not agree on pairings.

"The episode is currently available for free on Hulu.  The most relevant scene begins at about 8:20.  Later on, around 14:33, one member of the group even accuses others of strategically manipulating their preferences to suggest that he is unpopular. "

Buy and Sell First Dates (now we're just bargaining over the price)

That's the idea behind What's Your Price.com, a two sided dating platform in which Generous People (appears to be mostly guys) can negotiate a price to meet Attractive People (appears to be mostly girls). (It reminds me of the old joke whose punchline is "now we're just bargaining over the price."

How it works:Three Steps To Using WhatsYourPrice.com

• Fill out your profile and upload a photo...

  Your experience with WhatsYourPrice.com starts with filling out a profile about yourself, who you'd like to meet and what you expect on a first date. In order to use the website, you must have an approved profile, and at least one approve photo of yourself.

• Make an offer or accept an offer...

  Once you find the people you'd like to date, ask them out by making an offer. If you're a generous user, name the price you're willing to pay for the first date. And, if you're an attractive user, name the price you want to get paid for the first date. Our offer negotiating system will allow you to accept an offer, reject an offer, or counter with a different price.

• Send a message to setup a date!

  Once an offer is accepted, you're ready to plan the date. Simply write a message to schedule a time and place for your first date. It's simple and it's fun!

WhatsYourPrice.com First Date Etiquette

After you've accepted an offer for a first date, it's time to plan and schedule the first date. You may want to check out some of our first date ideas, but do try to be creative. The next thing you may be wondering is how does a generous user of the website go about paying an attractive user for the first date. Here are some general etiquette and rules regarding Do's and Don'ts.
* DO NOT pay or ask anyone for payment prior to meeting for a date
* If someone asks you to send money by Western Union, report them immediately
* Generous members are expected to pay for the date (there's no going dutch here)
* Our advice: Pay 50% of the date at the start of the date, and 50% at the end
* DO NOT accept personal checks or cashier's checks - there's just too much fraud
* CASH is king, and pay only when you meet your date in person


HT: James W. Boudreau

Brooklyn man pleads guilty to trafficking black market kidneys

Yesterday, in Trenton NJ, Brooklyn man pleads guilty to trafficking black market kidneys to N.J. residents

"The price was steep. As much as $160,000 to secure a donor willing to give up a human kidney for transplant.

"And Levy Itzhak Rosenbaum ... bragged on surveillance recordings that he had participated in many such black market deals.

"Today, the 60-year-old Israeli pleaded guilty in federal court to helping an FBI informant procure a kidney as part of an elaborate federal sting. At the same time, he admitted arranging transplants for three other New Jersey patients with failing kidneys — all of whom underwent surgery in out-of-state hospitals after paying Rosenbaum. None of the patients or hospitals was named, nor were they charged.

"It marked the first time in this country anyone has ever been convicted for brokering illegal kidney transplants for profit."
**********

See my earlier post on this case:

Monday, July 27, 2009

Corruption and kidneys in New Jersey and Brooklyn

***********

the Haaretz story is very good, so I'm quoting a lot of it below:
New York man pleads guilty to selling Israeli human organs

"His attorneys, Ronald Kleinberg and Richard Finkel, said in a statement that their client had performed a life-saving service for desperately ill people who had been languishing on official transplant waiting lists.

"The transplants were successful and the donors and recipients are now leading full and healthy lives," the statement said. "In fact, because of the transplants and for the first time in many years, the recipients are no longer burdened by the medical and substantial health dangers associated with dialysis and kidney failure."

"The lawyers added that Rosenbaum had never solicited clients, but that recipients had sought him out, and that the donors he arranged to give up kidneys were fully aware of what they were doing. The money involved, they argued, was for expenses associated with the procedures, which they claim were performed in prestigious American hospitals by experienced surgeons and transplant experts. The lawyers did not name the hospitals involved, nor are they named in court documents.

"Prosecutors argued that Rosenbaum was fully aware he was running an illicit and profitable operation - buying organs from vulnerable people in Israel for $10,000, and selling them to desperate, wealthy American patients.

"A black market in human organs is not only a grave threat to public health, it reserves lifesaving treatment for those who can best afford it at the expense of those who cannot," said New Jersey's U.S. Attorney, Paul Fishman. "We will not tolerate such an affront to human dignity."

"Each of the four counts carries a maximum five-year prison sentence plus a fine of up to $250,000. Rosenbaum also agreed to forfeit $420,000 in real or personal property that was derived from the illegal kidney sales.

...

"Although the hospitals where the operations Rosenbaum arranged have not been named, critics and experts on organ trafficking say many U.S. hospitals do not have vigorous enough procedures for looking into the source of the organs they transplant because such operations are lucrative.

...

"Under 1984 federal law, it is illegal for anyone to knowingly buy or sell organs for transplant. The practice is illegal just about everywhere else in the world, too.

"But demand for kidneys far outstrips the supply, with 4,540 people dying in the U.S. last year while waiting for a kidney, according to the United Network for Organ Sharing. As a result, there is a thriving black market for kidneys around the world.

"Art Caplan, the director of the Center for Bioethics at the University of Pennsylvania and a co-chairman of a United Nations task force on organ trafficking, said kidneys are the most common of all trafficked organs because they can be harvested from live donors, unlike other organs. He said Rosenbaum had pleaded guilty to one of the "most heinous crimes against another human being."

"Internationally, about one quarter of all kidneys appear to be trafficked," Caplan said. "But until this case, it had not been a crime recognized as reaching the United States."