Fair Division with Bounded Sharing: Binary and Non-Degenerate Valuations
Abstract
A set of objects is to be divided fairly among agents with different tastes, modeled by additive utility-functions. If we consider the objects as indivisible, many instances of the decision problem: ``Is there a fair division of the objects among the agents'' are negative. In addition, this question is hard to solve even for most of the special cases. The latter reasons give us a good motivation to relax the problem for which the running time complexity is better, and the number of positive instances (admitting a fair division) will significantly grow. Whereas many works relax the fairness criteria, this paper introduces another relaxation: an agent is allowed to share a \emph{bounded} number of objects between two or more agents in order to attain fairness. The paper studies various notions of fairness, such as proportionality, envy-freeness, equitability, and consensus. We analyze the run-time complexity of finding a fair allocation with a given number of sharings under several restrictions on the agents' valuations, such as: binary, generalized-binary, and non-degenerate.
Cite
@article{arxiv.1912.00459,
title = {Fair Division with Bounded Sharing: Binary and Non-Degenerate Valuations},
author = {Samuel Bismuth and Ivan Bliznets and Erel Segal-Halevi},
journal= {arXiv preprint arXiv:1912.00459},
year = {2025}
}
Comments
Full version of a paper accepted to SAGT 2024