Economists have lately been called upon not only to analyze markets, but to design them. Market design involves a responsibility for detail, a need to deal with all of a market’s complications, not just its principle features. Designers therefore cannot work only with the simple conceptual models used for theoretical insights into the general working of markets. Instead, market design calls for an engineering approach. Drawing primarily on the design of the entry level labor market for American doctors (the National Resident Matching Program), and of the auctions of radio spectrum conducted by the Federal Communications Commission, this paper makes the case that experimental and computational economics are natural complements to game theory in the work of design. The paper also argues that some of the challenges facing both markets involve dealing with related kinds of complementarities, and that this suggests an agenda for future theoretical research.

We report on the design of the new clearinghouse adopted by the National Resident Matching Program, which annually fills approximately 20,000 jobs for new physicians. Because the market has complementarities between applicants and between positions, the theory of simple matching markets does not apply directly. However, computational experiments show the theory provides good approximations. Furthermore, the set of stable matchings, and the opportunities for strategic manipulation, are surprisingly small. A new kind of “core convergence ” result explains this; that each applicant interviews only a small fraction of available positions is important. We also describe engineering aspects of the design process.

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The language of game theory—coalitions, payo¤s, markets, votes— suggests that it is not a branch of abstract mathematics; that it is motivated by and related to the world around us; and that it should be able to

In connection with an earlier paper on the exchange of live donor kidneys (Roth, Sönmez, and Ünver 2004) the authors entered into discussions with New England transplant surgeons and their colleagues in the transplant community, aimed at implementing a Kidney Exchange program. In the course of those discussions it became clear that a likely first step will be to implement pairwise exchanges, between just two patient-donor pairs, as these are logistically simpler than exchanges involving more than two pairs. Furthermore, the experience of these surgeons suggests to them that patient and surgeon preferences over kidneys should be 0-1, i.e. that patients and surgeons should be indierent among kidneys from healthy donors whose kidneys are compatible with the patient. This is because, in the United States, transplants of compatible live kidneys have about equal graft survival probabilities, regardless of the closeness of tissue types between patient and donor (unless there is a rare perfect match). In the present paper we show that, although the pairwise constraint eliminates some potential exchanges, there is a wide class of constrained-efficient mechanisms that are strategy-proof when patient-donor pairs and surgeons have 0-1 preferences. This class of mechanisms includes deterministic mechanisms that would accomodate the kinds of priority setting that organ banks currently use for the allocation of cadaver organs, as well as stochastic mechanisms that allow considerations of distributive justice to be addressed.

The deferred acceptance algorithm proposed by Gale and Shapley (1962) has had a profound influence on market design, both directly, by being adapted into practical matching mechanisms, and, indirectly, by raising new theoretical questions. Deferred acceptance algorithms are at the basis of a number of labor market clearinghouses around the world, and have recently been implemented in school choice systems in Boston and New York City. In addition, the study of markets that have failed in ways that can be fixed with centralized mechanisms has led to a deeper understanding of some of the tasks a marketplace needs to accomplish to perform well. In particular, marketplaces work well when they provide thickness to the market, help it deal with the congestion that thickness can bring, and make it safe for participants to act effectively on their preferences. Centralized clearinghouses organized around the deferred acceptance algorithm can have these properties, and this has sometimes allowed failed markets to be reorganized.

This paper studies matching in vertical networks, generalizing the theory of matching in two-sided markets. It gives sufficient conditions for the existence of stable networks and presents an algorithm for finding two of them. One is the best stable network for the agents on the “upstream ” end of an industry. The other is best for the agents on the “downstream ” end. The paper describes several properties of the set of stable networks and discusses applications of the theory to the design of matching markets with more than two types of agents and to the empirical analysis of supply chains. (JEL C78, D40)

The design of the New York City (NYC) High School match involved tradeoffs between incentives and efficiency, because some schools are strategic players that rank students in order of preference, while others order students based on large priority classes. Therefore it is desirable for a mechanism to produce stable matchings (to avoid giving the strategic players incentives to circumvent the match), but is also necessary to use tie-breaking for schools whose capacity is sufficient to accommodate some but not all students of a given priority class. We analyze a model that encompasses one-sided and two-sided matching models. We first observe that breaking indifferences the same way at every school is sufficient to produce the set of student optimal stable matchings. Our main theoretical result is that a student-proposing deferred acceptance mechanism that breaks indifferences the same way at every school is not dominated by any other mechanism that is strategy-proof for students. Finally, using data from the recent redesign of the NYC High School match, which places approximately 90,000 students per year, we document that the extent of potential efficiency loss is substantial. Over 6,800 student applicants in the main round of assignment could have improved their assignment in a (non strategy-proof) student optimal mechanism, if the same student preferences would have been revealed.

Abstract: This essay discusses some things we have learned about markets, in the process of designing marketplaces to fix market failures. To work well, marketplaces have to provide thickness, i.e. they need to attract a large enough proportion of the potential participants in the market; they have to overcome the congestion that thickness can bring, by making it possible to consider enough alternative transactions to arrive at good ones; and they need to make it safe and sufficiently simple to participate in the market, as opposed to transacting outside of the market, or having to engage in costly and risky strategic behavior. I'll draw on recent examples of market design ranging from labor markets for doctors and new economists, to kidney exchange, and school choice in New York City and Boston. 1 This paper was prepared to accompany the Hahn Lecture I delivered at the Royal Economic Society

In contrast to entry-level professional labor markets, in which cohorts of candidates and positions become available at the same time (e.g., when candidates graduate from school), senior level positions typically become available when an incumbent retires, or a new position is created, and when a senior position is filled a new vacancy is often created elsewhere. We model senior level labor markets as two-sided matching markets in which matchings are destabilized by retirements and new entries, and can return to stability by a decentralized process of offers and acceptances. This generalizes the standard analysis in a way which has points of contact with the sociological literature on vacancy chains.