When allocating indivisible items, there are various ways to use monetary transfers for eliminating envy. Particularly, one can apply a balanced vector of transfer payments, or charge each agent a positive amount, or -- contrarily -- give each agent a positive amount as a ``subsidy''. In each model, one can aim to minimize the amount of payments used; this aim translates into different optimization objectives in each setting. This note compares the various models, and the relations between upper and lower bounds for these objectives.
@article{arxiv.2506.18794,
title = {Fair Allocation with Money: What is Your Objective?},
author = {Noga Klein Elmalem and Rica Gonen and Erel Segal-Halevi},
journal= {arXiv preprint arXiv:2506.18794},
year = {2025}
}