Generalized Rental Harmony

Rental harmony is the problem of assigning rooms in a rented house to tenants with different preferences, and simultaneously splitting the rent among them, such that no tenant envies the bundle (room and price) given to another tenant. Various researchers have studied this problem mainly under two incompatible assumptions: the miserly tenants assumption—each tenant prefers a free room to a room with a positive price; and the quasilinear tenants assumption—each tenant attributes a monetary value to each room, and prefers a room of which the difference between value and price is maximum. This article shows that the main technique used for rental harmony with miserly tenants, using Sperner’s lemma, can be adapted to a much more general class of preferences, one that contains both miserly tenants and quasilinear tenants as special cases. As a corollary, some recent results derived for miserly tenants are found to be applicable to this more general class, too.