Large Matching Markets
Saturday, Jan. 6, 2018 8:00 AM - 10:00 AM
- Chair: SangMok Lee, University of Pennsylvania
The Cutoff Structure of Top Trading Cycles in School Choice
AbstractThe prominent Top Trading Cycles (TTC) mechanism has attractive properties for school choice, as it is strategy-proof, Pareto efficient, and allows school boards to guide the assignment by specifying priorities. However, the common combinatorial description of TTC does little to explain the relationship between student priorities and their eventual assignment. This creates difficulties in transparently communicating TTC to parents and in guiding policy choices of school boards.
We show that the TTC assignment can be described by an admission thresholds for each pair of schools, where n is the number of schools. These thresholds can be observed after mechanism is run, and can serve as non-personalized prices that allow students to verify their assignment.
In a continuum model these thresholds can be computed directly from the distribution of preferences and priorities, providing a framework that can be used to evaluate policy choices. We provide closed form solutions for the assignment under a family of distributions, and derive comparative statics. As an application of the model we solve for the welfare maximizing investment in school quality, and find that a more egalitarian investment can be more efficient because it promotes more efficient sorting by students.
Need Versus Merit: The Large Core of College Admissions Markets
AbstractWe study college admissions markets, where each college offers multiple levels of
financial aid. Colleges subject to budget and capacity constraints wish to recruit the best qualified students. Deferred Acceptance is strategy-proof for students, but the scope for manipulation by colleges is substantial, even in large markets. Successful manipulation takes the simple form of allocating funding based on need rather than merit. Stable allocations may differ in the number of assigned students. In Hungary, where the centralized college admissions clearinghouse uses Deferred Acceptance, another stable allocation would increase the number of students accepted to college by at least 3%, and applicants from low socioeconomic backgrounds would benefit disproportionately.
Top Trading Cycles in Two-Sided Matching Markets: An Irrelevance of Priorities in Large Matching Markets
- A1 - General Economics