An efficiency-adjusted fair mechanism for house allocation problem with existing tenants

We study a house allocation problem where there are both existing tenants and new applicants. The NH4 mechanism is a real-world allocation mechanism which satisfies individual rationality, fairness and strategy-proofness. But it fails Pareto efficiency. We propose an efficiency-adjusted NH4 mechanism that allows each student to consent a certain priority violation that has no effect on her own assignment. Under this mechanism, such consent can help recover efficiency loss which is caused by resolving squatting conflicts between two students. Moreover, we show which students' consents will be used.