Abstract
In this article we study a problem of fair division. In particular we study a notion introduced by J. Barbanel that generalizes super envy-free fair division. We call this notion hyper envy-free. We give a new proof for the existence of such fair divisions. Our approach relies on classical linear algebra tools and 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 inequality constraints?Furthermore, when all the measures are given with piecewise constant density functions then we show how to construct effectively such a fair division.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
