Fair Division with Prioritized Agents

TL;DR

This paper introduces a new fairness concept called EFPrior for indivisible item division, ensuring prioritized agents are envy-free while maintaining overall EF1, and provides polynomial algorithms for its computation.

Contribution

It proposes the EFPrior fairness notion, studies its existence, and develops polynomial algorithms for computing such allocations under general and special cases.

Findings

Simple round-robin algorithm works for additive valuations.

Polynomial algorithms are available for most items allocation.

Special cases allow for allocations when all items must be allocated.

Abstract

We consider the fair division problem of indivisible items. It is well-known that an envy-free allocation may not exist, and a relaxed version of envy-freeness, envy-freeness up to one item (EF1), has been widely considered. In an EF1 allocation, an agent may envy others' allocated shares, but only up to one item. In many applications, we may wish to specify a subset of prioritized agents where strict envy-freeness needs to be guaranteed from these agents to the remaining agents, while ensuring the whole allocation is still EF1. Prioritized agents may be those agents who are envious in a previous EF1 allocation, those agents who belong to underrepresented groups, etc. Motivated by this, we propose a new fairness notion named envy-freeness with prioritized agents "EFPrior", and study the existence and the algorithmic aspects for the problem of computing an EFPrior allocation. With additive valuations, the simple round-robin algorithm is able to compute an EFPrior allocation. In this paper, we mainly focus on general valuations. In particular, we present a polynomial-time algorithm that outputs an EFPrior allocation with most of the items allocated. When all the items need to be allocated, we also present polynomial-time algorithms for some well-motivated special cases.