重访二元杂务的EFX与fPO分配
Revisiting EFX and fPO Allocations for Binary Chores
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中文总结 AI 辅助
本文研究二元杂务的公平高效分配，提出新势函数与局部搜索算法实现不平等权利下的WEFX和fPO，并揭示不平等权利对两全其美保证的障碍。
中文摘要 AI 辅助
我们研究了在二元可加成本下不可分割杂务的公平且高效的分配，重点关注不平等权利和两全其美保证。虽然二元估值在商品领域已被广泛研究，但其在杂务方面的对应研究仍远未得到充分理解。一个显著的例外是Tao等人（TCS 2025）的工作，他们证明了在平等权利下，二元杂务的EFX和fPO是兼容的。我们重新审视了不平等权利下的二元杂务，并建立了满足WEFX和fPO的分配的计算方法。我们的关键技术贡献是一个针对杂务量身定制的新字典序势函数：任何最小化该势的分配都能同时保证WEFX和fPO。该势进一步指导了一种多项式时间的局部搜索算法，用于计算具有此类公平性和效率保证的分配。对于两全其美的保证，我们表明不平等权利会产生一个尖锐的障碍：即使只有两个智能体且具有相同的二元可加成本，也没有任何抽签能同时满足事前WEF和事后WEF1。相比之下，对于平等权利，我们在多项式时间内构造了一个抽签，该抽签事前满足EF和fPO，而每个实现都同时是EFX和fPO。
英文摘要
We study fair and efficient allocations of indivisible chores under binary additive costs, with a focus on unequal entitlements and best-of-both-worlds guarantees. While binary valuations have been extensively studied for goods, their chore counterpart remains much less understood. A notable exception is due to Tao et al. (TCS 2025), who established that EFX and fPO are compatible for binary chores with equal entitlements. We revisit binary chores under unequal entitlements and establish the computation of allocations that satisfy WEFX and fPO. Our key technical contribution is a new lexicographic potential function tailored to chores: any allocation minimizing this potential ensures both WEFX and fPO. This potential further guides a polynomial-time local-search algorithm for computing allocations with such fairness and efficiency guarantees. For best-of-both-worlds guarantees, we show that unequal entitlements create a sharp obstruction: even with two agents and identical binary additive costs, no lottery can simultaneously satisfy ex-ante WEF and ex-post WEF1. In contrast, for equal entitlements, we construct in polynomial time a lottery that is ex-ante EF and fPO, while every realization is both EFX and fPO.
发表机构
- University of Macau（澳门大学）
- Nanyang Technological University（南洋理工大学）
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