Speaker: Nick Arnosti (Columbia Business School, New York)
Title: A Continuum Model of Stable Matching with Finite Capacities
Abstract: We introduce a continuum model of stable matching. Whereas analyses of large finite markets make restrictive assumptions on priorities and preferences, and the continuum model of Azevedo and Leshno (2016) assumes large capacities, our model allows for arbitrary preferences, priorities and capacities.
Our model always has a unique stable outcome, which can be found using an analog of the Deferred Acceptance algorithm. The crucial difference between our model and that of Azevedo and Leshno (2016) is that they assume that the amount of student interest at each school is deterministic, whereas we assume that it follows a Poisson distribution. As a result, our model accurately predicts the simulated distribution of cutoffs, even for markets with only ten schools and twenty students.
We use our model to generate new insights about the number and quality of matches. When schools are homogeneous, we provide upper and lower bounds on students' average rank, which match results from Ashlagi et al (2017) but apply to more general settings. Our model also provides clean analytical expressions for the number of matches in a platform pricing setting considered by Marx and Schummer (2019).
Bio: Prof. Nick Arnosti, Ph.D., is an Assistant Professor at the Columbia Business School, Ney York, U.S.A. He received a PhD in Operations Research from Stanford University in 2016. His research focuses on the allocation of "social goods" which are given away, rather than sold to maximize profit. Examples include seats in public schools, affordable housing, permits for hiking and hunting, and discounted event tickets.
