The college admissions problem with a continuum of students

Authors:
Eduardo M. Azevedo;Jacob D. Leshno
Affiliations:
Harvard University, Cambridge, NJ, USA;Harvard University & Harvard Business School, Cambridge, MA, USA
Venue:
Proceedings of the 12th ACM conference on Electronic commerce
Year:
2011

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Abstract

In many two-sided matching markets, agents on one side are matched to a large number of agents on the other side (e.g. college admissions). Yet little is known about the structure of stable matchings when there are many agents on one side. We propose a variation of the Gale and Shapley [3] college admissions model where a finite number of colleges is matched to a continuum of students. It is shown that, generically (though not always) (i) there is a unique stable matching, (ii) this stable matching varies continuously with the underlying economy, and (iii) it is the limit of the set of stable matchings of approximating large discrete economies.