A polynomial algorithm for maxmin and minmax envy-free rent division on a soft budget

Document pages: 24 pages

Abstract: The current practice of envy-free rent division, lead by the fair allocationwebsite Spliddit, is based on quasi-linear preferences. These preferences ruleout agents well documented financial constraints. To resolve this issue weconsider piece-wise linear budget constrained preferences. These preferencesadmit differences in agents marginal disutility of paying rent below and abovea given reference, i.e., a soft budget. We construct a polynomial algorithm tocalculate a maxmin utility envy-free allocation, and other related solutions,in this domain.