发表机构
Indian Institute of Technology Kanpur（坎普尔印度理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明在负二分估值下，杂务分配可借助单位补贴实现无嫉妒且EF1，并给出紧界与多项式算法，但无法同时保证帕累托最优。
AI 中文摘要
我们研究了在负二分估值下，带补贴的不可分割杂务分配问题，其中每项杂务的边际负效用要么为零，要么为一。这是Barman等人（2022）的二分商品模型的杂务对应版本，在该商品模型中，已知每位代理人最多一单位补贴足以实现无嫉妒。我们证明，在仅假设二元边际效用、无其他结构假设的情况下，相同的最优保证对杂务也成立。对于每个具有负二分估值的实例，存在一个完整分配$A$和一个补贴向量$p\in\{0,1\}^n$，满足$\sum_{i\in N} p_i\le n-1$，使得$(A,p)$是无嫉妒的。此外，即使在支付补贴之前，分配$A$也是EF1的。该界是紧的，并且分配和补贴可以在值预言机模型中于多项式时间内计算得出。我们进一步表明，如果还要求帕累托最优性，则单位补贴保证通常无法维持。我们的算法从Tao等人（2025）的算法产生的无嫉妒部分分配开始，将剩余杂务分配给终端等式图的尾部强连通分量中的不同代理人，并通过相关等式图中的向后闭包来确定获得补贴的代理人。
英文摘要
We study the allocation of indivisible chores with subsidies under negative dichotomous valuations, where the marginal disutility of every chore is either zero or one. This is the chore analogue of the dichotomous goods model of Barman et al. (2022), for which a subsidy of at most one unit per agent is known to suffice for envy-freeness. We show that the same optimal guarantee holds for chores, under no structural assumption beyond binary marginals. For every instance with negative dichotomous valuations, there exists a complete allocation $A$ and a subsidy vector $p\in\{0,1\}^n$ with $\sum_{i\in N} p_i\le n-1$ such that $(A,p)$ is envy-free. Moreover, the allocation $A$ is EF1 even before subsidies are paid. The bound is tight, and the allocation and subsidies can be computed in polynomial time in the value-oracle model. We further show that the unit-subsidy guarantee cannot, in general, be maintained if Pareto optimality is also required. Our algorithm starts from an envy-free partial allocation produced by the algorithm of Tao et al. (2025), assigns the remaining chores to distinct agents in a tail strongly connected component of the terminal equality graph, and determines the subsidised agents through a backward closure in the associated equality graph.
Comments19 pages
