Leontief 偏好下不可分割物品的无嫉妒分配

中文摘要 AI 辅助

无嫉妒性是分配不可分割物品时公平性的一个基本概念。本文研究 Leontief 偏好（即完美互补模型）下的无嫉妒分配。尽管 Leontief 偏好已在可分割物品分配和市场均衡的背景下得到广泛研究，但在不可分割物品分配中受到的关注相对较少。我们证明，与基数偏好中的加性估值不同，当物品至少有两件时，Leontief 偏好下总是存在无嫉妒分配。相反，当只有一件物品时，无嫉妒分配可能不存在，但可以在多项式时间内判定。接下来，我们研究计算福利最大化的无嫉妒分配问题。我们证明该问题在一般情况下是 NP 难的，而当只有一件物品或所有智能体具有相同需求时，该问题可在多项式时间内求解。最后，我们研究了该问题的参数化复杂性。

英文摘要

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.

发表机构

• Indian Institute of Technology Jodhpur（印度焦浦尔理工学院）

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