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Large Matching Markets

Paper Session

Saturday, Jan. 6, 2018 8:00 AM - 10:00 AM

Marriott Philadelphia Downtown, Meeting Room 406
Hosted By: Econometric Society
  • Chair: SangMok Lee, University of Pennsylvania

Stable Matching in Large Economies​

Yeon-Koo Che
,
Columbia University
Jinwoo Kim
,
Seoul National University
Fuhito Kojima
,
Stanford University

Abstract

We study stability of two-side many to one two-sided many-to-one matching in which firms' preferences for workers may exhibit complementarities. Although such preferences are known to jeopardize stability in a finite market, we show that a stable matching exists in a large market with a continuum of workers, provided that each firm's choice changes continuously as the set of available workers changes. Building on this result, we show that an approximately stable matching exists in any large finite economy. We extend our framework to ensure a stable matching with desirable incentive and fairness properties in the presence of indifferences in firms' preferences.

The Cutoff Structure of Top Trading Cycles in School Choice

Jacob D. Leshno
,
Columbia University
Irene Lo
,
Columbia University

Abstract

The 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

Avinatan Hassidim
,
Bar-Ilan University
Assaf Romm
,
Hebrew University of Jerusalem
Ran I. Shorrer
,
Pennsylvania State University

Abstract

We 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

Yeon-Koo Che
,
Columbia University
Olivier Tercieux
,
Paris School of Economics

Abstract

TBD
Discussant(s)
Eduardo Azevedo
,
University of Pennsylvania
Utku Unver
,
Boston College
Scott Duke Kominers
,
Harvard University
Atila Abdulkadiroglu
,
Duke University
JEL Classifications
  • A1 - General Economics