发表机构
University of Toronto（多伦多大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在加性估值与拟阵约束下，针对三个智能体的层状拟阵正面解决了EF1分配的存在性问题，还扩展技术至四个智能体，同时证明横截拟阵等类别下EF1分配的存在性。
AI 中文摘要
我们研究加性估值和拟阵约束下不可分物品的公平分配问题。一个具有挑战性的开放问题是：在每个存在完整可行分配的拟阵下，是否都存在完整可行的无嫉妒至多一件物品（EF1）分配。Biswas和Barman[2018]的最新成果对划分拟阵正面解决了该问题。我们的首个成果是，当有三个智能体时，对推广了划分拟阵的层状拟阵正面解决了该问题。我们的技术将这一一般存在性问题归约为：在单个有限大小的关键层状拟阵下，寻找满足一个温和附加条件的EF1分配，我们通过案例分析确定了所需的分配。我们表明，我们的技术可一定程度扩展到四个智能体，将类似问题归约为在两个有限大小的层状拟阵下寻找EF1分配，尽管我们无法确定其存在性。我们还利用近期的拟阵分解结果，在更广泛的拟阵类别下确定EF1的存在性，具体而言，我们证明只要完整分配可行，横截拟阵下就始终存在EF1分配，并在更强假设下获得了图拟阵和gammoid的存在性结果。
英文摘要
We study fair allocation of indivisible goods under additive valuations and matroid constraints. A challenging open question is whether a complete and feasible envy-free up to one good (EF1) allocation exists under every matroid that admits a complete and feasible allocation. The state-of-the-art result by Biswas and Barman [2018] positively resolves this question for partition matroids. Our first result positively resolves it for laminar matroids, which generalize partition matroids, when there are three agents. Our technique reduces this general existence question to finding an EF1 allocation satisfying a mild additional condition under a single finite-sized key laminar matroid, and we establish the required allocation by case analysis. We show that our technique somewhat extends to four agents, reducing the analogous problem to finding EF1 allocations under two finite-sized laminar matroids, although we are unable to establish their existence. We also use recent matroid decomposition results to establish EF1 existence under broader classes of matroids. Specifically, we show that EF1 allocations always exist under transversal matroids whenever a complete allocation is feasible, and obtain existence results for graphic matroids and gammoids under stronger assumptions.
CommentsAccepted to ACM EAAMO 2026
