Strategyproof Matching with Minimum Quotas and Initial Endowments: (Extended Abstract).

Although minimum quotas are important in many real-world markets, existing strategyproof mechanisms require an unrealistic assumption that all students consider all schools acceptable (and vice-versa). We develop a strategyproof matching mechanism called Priority-List based Deferred Acceptance mechanism with Minimum Quotas (PLDA-MQ), which works under more realistic assumptions: (i) a student considers (at least) one particular school, which we call her initial endowment school, acceptable, and vice-versa, and (ii) the initial endowments satisfy all the minimum quotas. We require a matching to respect initial endowments; each student must be assigned to a school that is at least as good as her initial endowment. PLDA-MQ obtains the student-optimal matching within all matchings that respect minimum quotas/initial endowments and satisfies a stability requirement called Priority-List based (PL-) stability.