发表机构
University of Macau; Nanyang Technological University（澳门大学; 南洋理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究双值商品公平分配中最大纳什福利的近似保证，刻画其在EFX、PMMS和GMMS下的紧界，并证明三值实例中公平性显著恶化，确立强公平的边界。
AI 中文摘要
对于不可分割商品的公平分配，Caragiannis等人（2019）的里程碑式工作彻底改变了对最大纳什福利（MNW）分配的理解，揭示了其在平衡公平性（EF1）和效率（PO）方面对一般加性函数的“不合理”能力。后续工作表明，MNW分配在二元实例上同时满足EFX和GMMS（进而满足MMS和PMMS）（Amanatidis等人2021年和Barman等人2018年），并在双值实例上满足EFX（Amanatidis等人2021年）。在本文中，我们重新审视（个性化）双值实例，并提供MNW分配在EFX、PMMS和GMMS方面的近似保证的紧刻画，表明这些保证显著强于已知的一般估值情况。此外，我们证明即使在三值实例这一略微更一般的设置中，MNW的公平保证也会显著恶化，这为MNW分配强公平的实例确立了清晰的边界。
英文摘要
For the fair allocation of indivisible goods, the milestone work of Caragiannis et al. (2019) revolutionized the understanding of Maximum Nash Welfare (MNW) allocations by revealing their "unreasonable" ability to balance fairness (EF1) and efficiency (PO) for general additive functions. Subsequent work established that MNW allocations simultaneously satisfy EFX and GMMS (and consequently MMS and PMMS) for binary instances (Amanatidis et al. 2021 and Barman et al. 2018), and satisfy EFX for bi-valued instances (Amanatidis et al. 2021). In this paper, we revisit the (personalized) bi-valued instances and provide a tight characterization of the approximation guarantees of MNW allocations with respect to EFX, PMMS, and GMMS, showing that these guarantees are significantly stronger than what is known for general valuations. Furthermore, we demonstrate that even for the slightly more general setting of tri-valued instances, the fairness guarantees of MNW deteriorate significantly, which establishes a sharp boundary on the instances for which MNW allocations are strongly fair.
