Cutting a Cake Fairly for Groups Revisited
Theoretical Economics
2023-03-20 v1 Computer Science and Game Theory
Combinatorics
Abstract
Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to partition the players into groups of any desired size and divide the cake among the groups so that each group receives a single contiguous piece and every player is envy-free. For two groups, we characterize the group sizes for which such an assignment can be computed by a finite algorithm, showing that the task is possible exactly when one of the groups is a singleton. We also establish an analogous existence result for chore division, and show that the result does not hold for a mixed cake.
Cite
@article{arxiv.2301.09061,
title = {Cutting a Cake Fairly for Groups Revisited},
author = {Erel Segal-Halevi and Warut Suksompong},
journal= {arXiv preprint arXiv:2301.09061},
year = {2023}
}