Envy-Free Allocation of Indivisible Goods under Leontief Preferences

2026-09-23

AI Summary

本文研究了在Leontief偏好下不可分割物品的无嫉妒分配问题，证明了当至少有两种物品时总存在无嫉妒分配，并探讨了计算最大化福利的无嫉妒分配的复杂性。

Abstract

Envy-freeness is a fundamental notion of fairness in the allocation of indivisible goods. In this paper, we study envy-free allocation under Leontief preferences, which model perfect complements. Although Leontief preferences have been extensively studied in the context of allocating divisible goods and market equilibria, they have received comparatively little attention for the allocation of indivisible goods. We show that, unlike additive valuations in cardinal preferences, an envy-free allocation always exists for Leontief preferences when there are at least two goods. In contrast, envy-free allocations may fail to exist when there is a single good, however it can be decided in polynomial time. We next study the problem of computing a welfare-maximizing envy-free allocation. We prove that this problem is NP-hard in general, whereas it is polynomial-time solvable when there is only a single good or agents have identical demands. Finally, we investigate the parameterized complexity of this problem.

Problem

• Envy-freeness
• Indivisible Goods
• Leontief Preferences
• Welfare Maximization

Innovation

• Envy-free Allocation
• Leontief Preferences
• Indivisible Goods
• Welfare Maximization
• Parameterized Complexity