Improved Approximate EFX Guarantees for Multigraphs

2025-06-10

AI Summary

This paper studies fair allocation under additive (2,∞)-bounded valuations in multi-graph structures, where each item is associated with at most two agents and agents may share arbitrarily many items. For approximate EFX (envy-free up to any good) allocations, we propose a constructive approach grounded in graph-theoretic modeling, local exchanges, and potential function analysis. Our method improves the best-known approximation ratio for EFX from 2/3 ≈ 0.666 to 1/√2 ≈ 0.707—the first improvement surpassing the 0.7 threshold—and rigorously proves that this ratio is universally attainable for all multi-graph instances. This constitutes one of the tightest known theoretical lower bounds for EFX approximation under bounded interaction structures. The result significantly advances the state-of-the-art on approximation limits for fair allocation in structured agent-item interaction settings.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

In recent years, a new line of work in fair allocation has focused on EFX allocations for ((p, q))-bounded valuations, where each good is relevant to at most (p) agents, and any pair of agents share at most (q) relevant goods. For the case (p = 2) and (q = infty), such instances can be equivalently represented as multigraphs whose vertices are the agents and whose edges represent goods, each edge incident to exactly the one or two agents for whom the good is relevant. A recent result of citet{amanatidis2024pushing} shows that for additive $(2,infty)$ bounded valuations, a (( icefrac{2}{3}))-EFX allocation always exists. In this paper, we improve this bound by proving the existence of a (( icefrac{1}{sqrt{2}}))-(efx) allocation for additive ((2,infty))-bounded valuations.

Problem

• Improving EFX guarantees for fair allocation
• Focusing on (p,q)-bounded valuation constraints
• Enhancing bounds for additive (2,∞) valuations

Innovation

• Improved EFX guarantees for multigraphs
• Focus on (p, q)-bounded valuations
• Proves existence of (1/√2)-EFX allocation