We develop a theory of stability in many-to-many matching markets. We give conditions under which the setwise-stable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwise-stable set coincides with the pairwise-stable set and with the predictions of a non-cooperative bargaining model. The setwise-stable set possesses the conflict/coincidence of interest properties from many-to-one and one-to-one models. The theory parallels the standard theory of stability for many-to-one, and one-to-one, models. We provide results for a number of core-like solutions, besides the setwise-stable set.

We develop an index of segregation based on two premises: (1) a measure of segregation should disaggregate to the level of individuals, and (2) an individual is more segregated the more segregated are the agents with whom she interacts. We present an index that satisfies (1) and (2) and that is based on agents' social interactions: the extent to which blacks interact with blacks, whites with whites, etc. We use the index to measure school and residential segregation. Using detailed data on friendship networks, we calculate levels of within-school racial segregation in a sample of U. S. schools. We also calculate residential segregation across major U. S. cities, using block-level data from the 2000 U. S. Census.

We introduce a measure of the severity of violations of the revealed preference axioms, the money pump index (MPI). The MPI is the amount of money one can extract from a consumer who violates the axioms. It is also a statistical test for the hypothesis that a consumer is rational when behavior is observed with error. We present an application using a panel data set of food expenditures. The data exhibit many violations of the axioms. Mostly, the MPI for these violations is small. The MPI indicates that the hypothesis of consumer rationality cannot be rejected.

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We characterize choice rules for schools that regard students as substitutes while expressing preferences for a diverse student body. The stable (or fair) assignment of students to schools requires the latter to regard the former as substitutes. Such a requirement is in conflict with the reality of schools' preferences for diversity. We show that the conflict can be useful, in the sense that certain unique rules emerge from imposing both considerations. We also provide welfare comparisons for students when different choice rules are employed.