Matching with Quotas

We characterize the set of solutions for the many-to- many matching problem with quotas using centralized and decentralized mechanisms. Decentralized mechanism is a simple bargaining game in which courses proposes to the students they want and students choose the most preferred courses from the observed set of proposals. Centralized mechanism is an iterative procedure such that at every stage every agent (meaning course or student) chooses the most preferred set of partners over those who prefer the agent to the current match. Usual conditions on preferences used in the literature can not be applied for the problem with quotas. However, the generalizations of them can be used to together with restrictions on the space of matchings can sucesfully guarantee the characterization of the sets of stable matchings using centralized and decentralized mechanisms