Characterizing nonatomic admissions markets

TL;DR

This paper develops a model to predict student distribution across schools in both centralized and decentralized admissions markets, linking stable assignment with market dynamics and providing practical demand estimates.

Contribution

It introduces a characterization that connects stable assignment mechanisms with decentralized market equilibria, enabling explicit demand curve computation without detailed student data.

Findings

Accurately ranks university popularity in the US.

Provides demand curve estimates without granular student data.

Shows stable assignments as equilibria in decentralized markets.

Abstract

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 t\^{a}tonnement. 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.