Chapters 5 and 6 will explore models of many-to-one matching. In terms of the economic phenomena that motivate the models in this book, many to- one matching in two-sided markets is perhaps the most typical case, where one side of the market consists of institutions and the other side of individuals. Thus colleges admit many students, firms hire many workers, and hospitals employ many interns, all at the same time. But students typically attend only one college (at least at any given time), and so forth.

A central issue in formulating a model of many-to-one matching will be how to model the preferences of the institutions, since these involve comparisons of different groups of students, workers, and so on. No comparable question arose in the marriage model, where preferences over individuals were sufficient to determine preferences over matchings. We will see that there are both important differences and striking similarities between one-to-one and many-to-one matching. The results presented in Chapter 5 will also complete the explanation begun in Section 1.1 of the phenomena described there concerning the labor market for medical interns. And some further empirical observations in related markets will briefly be described.