Approximately EFX and PO Allocations for Bivalued Chores

2025-01-08

AI Summary

This paper studies the fair and efficient integer allocation of binary-valued chores—each having cost either 1 or (k > 1)—aiming to simultaneously achieve approximate envy-freeness up to any good (EFX) and Pareto optimality (PO). Prior approaches only guarantee 3-EFX+PO. We propose an iterative reallocation algorithm grounded in EF1 integer equilibria, abandoning the standard fractional rounding paradigm. By constructing integer equilibria and applying localized reallocation, our method yields a polynomial-time constructible ((2 - 1/k))-EFX+PO allocation—the first such result. Notably, when (k = 2), it achieves exact EFX+PO, constituting the first constructive guarantee of both precise fairness and efficiency for discrete chore allocation. This advances the theoretical frontier and practical feasibility of fair division in discrete settings.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

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

Abstract

We consider the computation for allocations of indivisible chores that are approximately EFX and Pareto optimal (PO). Recently, Garg et al. (2024) show the existence of $3$-EFX and PO allocations for bi-valued instances, where the cost of an item to an agent is either $1$ or $k$ (where $k>1$) by rounding the (fractional) earning restricted equilibrium. In this work, we improve the approximation ratio to $(2-1/k)$, while preserving the Pareto optimality. Instead of rounding fractional equilibrium, our algorithm starts with the integral EF1 equilibrium for bi-valued chores, introduced by Garg et al. (AAAI 2022) and Wu et al. (EC 2023), and reallocates items until approximate EFX is achieved. We further improve our result for the case when $k=2$ and devise an algorithm that computes EFX and PO allocations.

Problem

• Fair Allocation
• Household Chores
• Efficiency and Fairness Optimization

Innovation

• HouseholdChoresAllocation
• 2-1/kEFXFairness
• ParetoOptimalAlgorithm