College Admissions with Complementarities

We study many-to-one matching with complementarities. Real life examples include college admissions with two-sided monetary transfers, teacher assignment with different teaching loads, worker assignment. Due to the presence of complementarities, the conditions that are essential for the existence of stable allocation fail. Despite this failure, we provide conditions to guarantee the existence of stable allocation. To our knowledge this is the first paper obtaining positive result related to existence of (group) stable matching and existence of strategy-proof and (group) stable mechanism in the presence of complementarities