AI 中文总结
该研究针对不可分割杂务的期望可信分配问题，提出首个具备常数倍事后MMS近似保证的TIE机制，同时收紧了不同智能体数量下的近似比下界。
AI 中文摘要
我们研究用于分配不可分割杂务、同时提供事后最大最小份额（MMS）保证的期望可信（TIE）机制。对于物品分配场景，Bu和Tao（FOCS 2025）确立了TIE机制的(1/n)近似比，Babaioff、Feige与Manaker Morag（FOCS 2026）随后将其大幅改进为Ω(1/log n)近似比，其中n为智能体数量。杂务分配的对应问题受到的关注较少，目前已知的最优结果由Aziz、Li和Wu（MAPR 2024）提出，他们给出了一种TIE机制，其MMS近似保证为O(√log n)，且仅在期望意义下成立；他们还确立了双智能体场景下TIE机制的6/5下界。本文提出了首个能实现常数倍事后MMS近似保证的杂务分配TIE机制。具体而言，我们的机制对任意数量n的智能体都能保证1.97的事后比率，当n=2时该比率提升至4/3，n=3时提升至3/2。在难度方面，我们将双智能体的下界收紧至4/3，证明了我们的机制在n=2时是最优的。更一般地，我们确立了对于所有n≥3，TIE机制可达到的事后MMS近似比的13/12下界。
英文摘要
We study truthful-in-expectation (TIE) mechanisms for allocating indivisible chores alongside ex-post maximin share (MMS) guarantees. For goods, Bu and Tao (FOCS 2025) established a (1/n)-approximation for TIE mechanisms, and this was substantially improved by Babaioff, Feige, and Manaker Morag (FOCS 2026), who established an Ω(1/\log n) approximation, where n is the number of agents. The corresponding problem for chores has received less attention. The best-known result is due to Aziz, Li, and Wu (MAPR 2024), who gave a TIE mechanism with an O(\sqrt{\log n}) MMS approximation guarantee that holds only in expectation. They also established a 6/5 lower bound for TIE mechanisms for two agents. In this paper, we present the first TIE mechanism for chores that achieves a constant ex-post MMS approximation guarantee. Specifically, our mechanism guarantees an ex-post ratio of 1.97 for any number of agents n, which improves to 4/3 for n=2 and 3/2 for n=3. On the hardness side, we tighten the two-agent lower bound to 4/3, showing that our mechanism is optimal for n=2. More generally, we establish a lower bound of 13/12 on the ex-post MMS approximation ratio achievable by TIE mechanisms for every n\ge 3.
Comments35 pages, 6 figures
