A 1.5-Sided Matching Problem : The Cost-Efficient House Allocation Problem with Existing Tenants

In this paper, we consider a house allocation with existing tenants model in which each transaction is costly for the central authority, a housing office. We compare two widely studied mechanisms, deferred acceptance (DA) and top trading cycles (TTC), based on their costs for the housing offices. A mechanism in which more existing tenants are assigned to their current house is preferred for the housing offices due to the costs of moving. We show that although there is no dominance between the two mechanisms, DA has more desirable features in terms of the cost efficiency for the housing offices. Then we include the welfare of the housing office in the welfare analysis and redefine the Pareto efficiency notion. We show that every fair matching is Pareto efficient. Based on the extended Pareto efficiency definition, the DA mechanism is the unique Pareto efficient, fair, and strategy-proof mechanism