Fair distributions for more participants than allocations

TL;DR

This paper investigates fair distribution methods for scenarios with more participants than available resources, extending classical cake-cutting results to accommodate secretive guests and robustness against guest removal.

Contribution

It introduces new conditions for envy-free distributions in over-participant settings, relaxing demand constraints from classical cake-cutting theories.

Findings

Conditions for envy-free distributions are weakened compared to classical results.

Extensions include handling secretive guests and robustness to removal of small guest sets.

Provides theoretical foundations for fair division with more participants than resources.

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.