Envy-Freeness in House Allocation Problems
arXiv:1905.00468 · doi:10.1016/j.mathsocsci.2019.07.005
Abstract
We consider the house allocation problem, where houses are to be assigned to agents so that each agent gets exactly one house. We present a polynomial-time algorithm that determines whether an envy-free assignment exists, and if so, computes one such assignment. We also show that an envy-free assignment exists with high probability if the number of houses exceeds the number of agents by a logarithmic factor.