Fair distributions for more participants than allocations
Abstract
We study the existence of fair distributions when we have more guests than pieces to allocate, focusing on envy-free distributions among those who receive a piece. The conditions on the demand from the guests can be weakened from those of classic cake-cutting and rent-splitting results of Stromquist, Woodall, and Su. We extend existing variations of the cake-cutting problem with secretive guests and those that resist the removal of any sufficiently small set of guests.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.