Brownbag Seminars: College Admissions with Complementarities

Abstract: We study many-to-one matching problem with complementarities. Real life examples include college admissions with two-sided monetary transfers, faculty recruitment with differentiated teaching loads, and worker assignment with various shifts. Due to the presence of complementarities, the conditions that are essential for the existence of stable allocation may fail. Despite this failure, we provide conditions to guarantee the existence of stable allocation for any problem.