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This paper investigates a class of matching problems—the assignment of indivisible items to agents where some agents have prior claims to some of the items. As a running example, we will refer to the indivisible items as houses. House allocation problems are not only of theoretical interest, but also of practical importance. A house allocation mechanism assigns a set of houses (or offices, tasks, etc.) to prospective tenants, allotting at most one house to each tenant. Rents are exogenously given and there is no medium of exchange, such as money. In general some houses will have existing tenants, some houses will be empty, and some applicants for housing will be new (e.g., freshmen). The canonical examples are assignment of college students to dormitory rooms and public housing units. Other examples are assignment of offices and tasks to individuals. Many universities in the United States employ some variant of a mechanism called the random serial dictatorship with squatting rights (RSD) to allocate dormitory rooms. Each existing tenant can either keep her house or enter the applicant pool. Each applicant is randomly
Chen et al. (Fri,) studied this question.