Fair Rent Division on a Budget Revisited

Stéphane Airiau, Hugo Gilbert, Umberto Grandi, Jérôme Lang, Anaëlle Wilczynski

Abstract: Rent division consists in simultaneously computing an allocation of rooms to agents and a payment, starting from an individual valuation of each room by each agent. When agents have budget limits, it is known that envy-free solutions do not necessarily exist. We propose two solutions to overcome this problem. In the first one, we relax envy-freeness to account for budget disparities. In the second one, we allow fractional allocations, in which agents may change rooms during the duration of the lease.