AI 中文总结
研究不可分割物品的时间公平分配，提出动态回溯框架实现强二元估值的精确TEFX，通过字典序势函数论证其能解决时间嫉妒循环并终止于有限时间，还确定了α - TEFX近似比率及TEFX和TMMS的不可能性结果。
AI 中文摘要
本文研究时间公平分配，即物品在多轮中分配且代理随时间要求累积公平性。关注经典公平概念的动态扩展：任意物品的时间无嫉妒性（TEFX）、其α - TEFX近似以及时间最大最小份额（TMMS）。由于这些严格公平标准通常无法满足，在约束下分析模型以界定可行与不可行的边界。贡献在于系统地描绘这些时间公平概念的结构边界。主要技术成果引入新颖的动态回溯框架，对强二元估值实现精确TEFX。通过字典序势函数论证证明，这种有界历史重新分配能系统解决时间嫉妒循环并在有限时间内终止。最后，确定相同估值和双值物品下α - TEFX的紧密近似比率，以及TEFX和TMMS的针对性不可能性结果，明确时间公平在数学上无法实现的地方，并恰当定位仅隐含满足新定义TMMS度量的先前算法。
英文摘要
This paper investigates temporal fair division, a setting where items are allocated over multiple rounds and agents require cumulative fairness over time. We focus on dynamic extensions of classic fairness notions: Temporal Envy-Freeness Up to Any Good (TEFX), its $α$-TEFX approximation, and Temporal Maximin Share (TMMS). Because these strict fairness criteria are known to be generally impossible to satisfy, we analyze the model under constraints to map the boundary between what is possible and what is not. Our contribution systematically maps the structural boundaries of these temporal fairness notions. Our main technical result introduces a novel dynamic backtracking framework that achieves exact TEFX for Strong Binary Valuations. We prove, via a lexicographical potential function argument, that this bounded historical reallocation systematically resolves temporal envy cycles and terminates in finite time. Finally, we establish tight approximation ratios for $α$-TEFX under identical valuations and bi-valued goods, alongside targeted impossibility results for TEFX and TMMS, demonstrating exactly where temporal fairness is mathematically unattainable, and properly contextualizing prior algorithms that only implicitly satisfied our newly defined TMMS metric.
CommentsAccepted to International Symposium on Algorithmic Game Theory (SAGT) 2026; 26 Pages
