How to cut a cake with a gram matrix
Computer Science and Game Theory
2017-07-11 v1 Multiagent Systems
Abstract
In this article we study the problem of fair division. In particular we study a notion introduced by J. Barbanel that generalizes super envy-free fair division. We give a new proof of his result. Our approach allows us to give an explicit bound for this kind of fair division. Furthermore, we also give a theoretical answer to an open problem posed by Barbanel in 1996. Roughly speaking, this question is: how can we decide if there exists a fair division satisfying some inequalities constraints? Furthermore, when all the measures are given with piecewise constant density functions then we show how to construct effectively such a fair division.
Cite
@article{arxiv.1707.02871,
title = {How to cut a cake with a gram matrix},
author = {Guillaume Chèze and Luca Amodei},
journal= {arXiv preprint arXiv:1707.02871},
year = {2017}
}