具有常数最大最小份额保证的期望真实机制

中文摘要 AI 辅助

我们研究了将不可分割物品真实且公平地分配给具有加性估值的n个策略性智能体的问题。Babaioff、Feige和Manaker Morag[FOCS 2026]提出了一种仅利用智能体对物品排序的随机机制，该机制满足期望真实（truthful in expectation, TIE），并在每次实现的分配中保证每个智能体获得其最大最小份额（maximin share, MMS）的1/(H_{n-1}+2)=Θ(1/log n)，其中H_{n-1}是第(n-1)个调和数；这几乎是仅使用排序信息所能达到的最优结果。他们推测，基数信息能让TIE机制实现常数级的事后MMS保证。我们证实了这一猜想：我们的TIE机制在每次实现的分配中，保证每个智能体至少获得其MMS的1/7；此外，该机制满足事前无嫉妒，且可在多项式时间内实现。\n我们的机制包含两个关键技术要素，二者都可能具有独立研究价值。第一个是真实的分数分配规则，用于确定每个智能体获得每件物品的概率：该规则在智能体排名前n-1的物品上给予其偏好，且每有另一个将该物品也排在自身前n-1名的智能体，就降低该智能体获得这件物品的概率。第二个是平衡边着色：我们将这些概率分解为从智能体到高价值物品的等概率匹配（仅高价值物品就能满足智能体的保证要求），并在不改变任何边际概率的前提下，以细粒度方式平衡这些匹配，使得任何未获得高价值物品的智能体都能从剩余物品中获得足够价值，同时不会出现任何物品分配过量的情况。

英文摘要

We study the truthful and fair allocation of indivisible goods to $n$ strategic agents with additive valuations. Babaioff, Feige, and Manaker Morag [FOCS 2026] gave a randomized mechanism that uses only the agents' rankings of the goods, is truthful in expectation (TIE), and guarantees every agent $1/(H_{n-1}+2)=Θ(1/\log n)$ of her maximin share (MMS) in every realized allocation, where $H_{n-1}$ is the $(n-1)$th harmonic number; this is nearly the best possible with rankings alone. They conjectured that cardinal information allows TIE mechanisms to achieve a constant ex-post MMS guarantee. We confirm this conjecture: our TIE mechanism guarantees every agent at least $1/7$ of her MMS in every realized allocation; moreover, the mechanism is ex-ante envy-free and can be implemented in polynomial time. Our mechanism has two key technical ingredients, both of which may be of independent interest. The first is a truthful fractional allocation rule specifying each agent's probability of receiving each good: it favors each agent on her top $n-1$ goods and reduces her probability of receiving a good for each other agent who also ranks it among her top $n-1$ goods. The second is the balanced edge coloring: we decompose these probabilities into equally likely matchings from agents to high-value goods, those that alone meet an agent's guarantee, and balance these matchings in a fine-grained way without changing any marginal probability, so that every agent who receives no high-value good can obtain sufficient value from the remaining goods without over-allocating any good.

发表机构

• Central China Normal University（华中师范大学）
• Shanghai Jiao Tong University（上海交通大学）
• The Hong Kong Polytechnic University（香港理工大学）

机构由 AI 辅助整理，请以论文原文为准。