Fair division with unequal shares is an intensively studied resource allocation problem. For $i\in [n] $, let $\mu_i $ be an atomless probability measure on the measurable space $(C,\mathcal{S})$ and let $t_i$ be positive numbers (entitlements) with $\sum_{i=1}^{n}t_i=1$. A fair division is a partition of $C$ into sets $S_i\in \mathcal{S} $ with $\mu_i(S_i)\geq t_i$ for every $i\in [n]$. We introduce new algorithms to solve the fair division problem with irrational entitlements. They are based on the classical Last diminisher technique and we believe that they are simpler than the known methods. Then we show that a fair division always exists even for infinitely many players.
@article{10_37236_10897,
author = {Zsuzsanna Jank\'o and Attila Jo\'o},
title = {Cutting a cake for infinitely many guests},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {1},
doi = {10.37236/10897},
zbl = {1484.91226},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10897/}
}
TY - JOUR
AU - Zsuzsanna Jankó
AU - Attila Joó
TI - Cutting a cake for infinitely many guests
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/10897/
DO - 10.37236/10897
ID - 10_37236_10897
ER -
%0 Journal Article
%A Zsuzsanna Jankó
%A Attila Joó
%T Cutting a cake for infinitely many guests
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/10897/
%R 10.37236/10897
%F 10_37236_10897
Zsuzsanna Jankó; Attila Joó. Cutting a cake for infinitely many guests. The electronic journal of combinatorics, Tome 29 (2022) no. 1. doi: 10.37236/10897
