CS-ECON Seminar Series

The Simple Structure of Top Trading Cycles in School Choice: A Continuum Model (Joint with Irene Lo)

Speaker:Jacob Leshno (Columbia)
Date: Friday, February 24, 2017
Time: 12:00pm - 1:00pm
Location: Gross 318, Duke

Abstract

Many cities determine the assignment of students to schools through a school choice mechanism which calculates an assignment based on student preferences and school priorities. The prominent Top Trading Cycles (TTC) algorithm is strategy-proof and Pareto efficient, but the combinatorial description of TTC makes it non-transparent to parents and difficult to analyze for designers. We give a tractable characterization of the TTC mechanism for school choice: the TTC assignment can be simply described by n^2 cutoffs, where n is the number of schools. We define TTC in a continuum model, in which these thresholds can be directly calculated by a differential equation. The model also allows us to compute comparative statics, analyze sequential trade procedures, and show that changes in the priority structure can have non-trivial indirect effects on the allocation. We also apply this model to solve for optimal investment in school quality, and help explain empirical findings about the relation between the TTC assignment and the Deferred Acceptance assignment. To validate the continuum model we show that it gives a good approximation for strongly converging economies. Our analysis draws on an interesting connection between continuous trading procedures and continuous time Markov chains.

Biography

Jacob Leshno is an Assistant Professor in the Decision, Risk & Operations group in the Graduate School of Business, Columbia University. His research focus is matching theory and market design, studying how to create rules that lead to efficient allocation of resources or effective matching between workers and employers, assignment of students to schools, or patients to nursing homes. Jacob holds a PhD in economics from Harvard University, completed under the supervision of Prof. Alvin Roth. Prior to joining Columbia he spent a year as a post-doc researcher in Microsoft Research New England. He holds an M.Sc. and B.Sc. in pure math from Tel Aviv University.

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