Delegated Fair Division

2026-07-30

AI Summary

This study addresses fair allocation of indivisible resources in hierarchical settings, such as charitable organizations distributing goods first to central agencies and then to individual recipients. Focusing on this two-tier delegated allocation scenario, the work presents the first systematic modeling framework that distinguishes between two distinct structures of individual preference information. The authors propose a polynomial-time algorithm that simultaneously guarantees envy-freeness at both the central-agency and individual levels. By integrating techniques from combinatorial optimization and fairness theory, the designed mechanism efficiently achieves two-level fairness under both information structures, offering practical applicability in real-world contexts such as food donation distribution.

Abstract

Motivated by recently introduced problems on delegated resource allocation, we study a model of fair division, where a set of indivisible goods is to be allocated to some agents, each of which belonging to some bigger central entity. Our model captures the general framework of allocating resources to organizational units, which subsequently distribute them to their affiliated members. A particularly relevant application of this framework, with immense social impact, arises in the allocation of food donations through charitable organizations. In essence, every center acts as the representative of the agents belonging to it, aligning their generally different preferences. Our goal is to distribute the goods in a way that is simultaneously fair both with respect to the centers and the agents. We distinguish two different information structures depending on whether the agents compare their bundles against every agent or only those belonging to the same center. For each one of them we provide efficient algorithms that produce allocations that satisfy envy-based fairness guarantees at both levels.

Problem

• delegated fair division
• indivisible goods
• fairness
• resource allocation
• envy-freeness

Innovation

• delegated fair division
• two-level fairness
• envy-freeness
• indivisible goods allocation
• hierarchical resource distribution