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.

In the context of entry-level labor markets, we consider the potential transactions that have to be evaluated before equilibrium transactions can be identified. These potential transactions involve offers that are rejected. After an initial phase in which many offers can be proffered in parallel, subsequent potential transactions must be processed serially, since a new offer cannot be made until an outstanding offer is rejected. In this phase even a small time required to process offers and rejections may cause bottlenecks. In many, perhaps most, decentralized labor markets, this means that transactions have to be finalized before there is time for the market to clear, that is, before all the potential transactions that would need to be evaluated in order to reach a stable outcome can in fact be evaluated. This has implications for the strategic behavior of firms and workers. In particular, in deciding to whom to offer a position, a firm may have strong incentives to consider not only its preferences over workers but also the likelihood that its offer will be accepted, since if its offer is rejected it may find that many other potential employees have become unavailable in the interim. The analysis is carried out in connection with the decentralized

This paper examines the determinants of assets at marriage in rural Ethiopia. We identify and test three separate processes that determine assets brought to marriage: assortative matching, compensating parental transfers at marriage, and strategic behavior by parents. We find ample evidence for the first, none for the second, and some evidence of the third for brides. We also find no evidence of competition for parental assets among siblings. Results suggest that parents do not transfer wealth to children in ways that compensate for marriage market outcomes. Certain parents, however, give more assets to daughters whenever doing so increases the chances of a daughter marrying a wealthy groom.

Baïou and Balinski (2000) characterized the stable admissions polytope using a system of linear inequalities. The structure of feasible solutions to this system of inequalities —fractional stable matchings—is the focus of this paper. The main result associates a geometric structure with each fractional stable matching. This insight appears to be interesting in its own right, and can be viewed as a generalization of the lattice structure (for integral stable matchings) to fractional stable matchings. In addition to obtaining simple proofs of many known results, the geometric structure is used to prove the following two results: first, it is shown that assigning each agent their “median ” choice among all stable partners results in a stable matching, which can be viewed as a “fair ” compromise; second, sufficient conditions are identified under which stable matchings exist in a problem with externalities, in particular, in the stable matching problem with couples. 1