We study the fair division of indivisible items with subsidies among n agents, where the absolute marginal valuation of each item is at most one. Under monotone valuations (where each item is a good), Brustle et al. (2020) demonstrated that a maximum subsidy of 2(n−1) and a total subsidy of 2(n−1)2 are sufficient to guarantee the existence of an envy-freeable allocation. In this paper, we improve upon these bounds, even in a wider model. Namely, we show that, given an EF1 allocation, we can compute in polynomial time an envy-free allocation with a subsidy of at most n−1 per agent and a total subsidy of at most n(n−1)/2. Moreover, we present further improved bounds for monotone valuations.
@article{arxiv.2308.11230,
title = {Towards Optimal Subsidy Bounds for Envy-freeable Allocations},
author = {Yasushi Kawase and Kazuhisa Makino and Hanna Sumita and Akihisa Tamura and Makoto Yokoo},
journal= {arXiv preprint arXiv:2308.11230},
year = {2023}
}