2021/07/03 by Max Kapur, Kapur, Max
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Advanced Causal Inference Techniques #Algorithm #Artificial intelligence #Auction Theory and Applications #Characterization (materials science) #Class (philosophy) #Computation #Computer science #Distribution (mathematics) #FOS: Economics and business #Game Theory and Voting Systems #Invertible matrix #Mathematical economics #Mathematical optimization #Mathematics #Parametric statistics #Ranking (information retrieval) #Set (abstract data type) #Statistics #Theoretical Economics (econ.TH) #econ.TH
paper · pdf · doi:10.48550/arxiv.2107.01340
published in arXiv (Cornell University) (Cornell University) · 47 pages, 10 figures
arxiv created 2021/07/03 · openalex publication_date 2021/07/03 · arxiv updated 2021/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article proposes a characterization of admissions markets that can predict the distribution of students at each school or college under both centralized and decentralized admissions paradigms. The characterization builds on recent research in stable assignment, which models students as a probability distribution over the set of ordinal preferences and scores. Although stable assignment mechanisms presuppose a centralized admissions process, I show that stable assignments coincide with equilibria of a decentralized, iterative market in which schools adjust their admissions standards in pursuit of a target class size. Moreover, deferred acceptance algorithms for stable assignment are a special case of a well-understood price dynamic called tâtonnement. The second half of the article turns to a parametric distribution of student types that enables explicit computation of the equilibrium and is invertible in the schools' preferability parameters. Applying this model to a public dataset produces an intuitive ranking of the popularity of American universities and a realistic estimate of each school's demand curve, and does so without imposing an equilibrium assumption or requiring the granular student information used in conventional logistic regressions.