House allocation refers to the problem where m houses are to be allocated to n agents so that each agent receives one house. Since an envy-free house allocation does not always exist, we consider finding such an allocation in the presence of subsidy. We show that computing an envy-free allocation with minimum subsidy is NP-hard in general, but can be done efficiently if m differs from n by an additive constant or if the agents have identical utilities.
@article{arxiv.2403.01162,
title = {Envy-Free House Allocation with Minimum Subsidy},
author = {Davin Choo and Yan Hao Ling and Warut Suksompong and Nicholas Teh and Jian Zhang},
journal= {arXiv preprint arXiv:2403.01162},
year = {2024}
}