平均每人四分之一（美元）确保比例性
One Quarter Each (on Average) Ensures Proportionality
AI总结：
本文研究不可分物品在补贴下的公平分配问题，证明在可加成本函数下，n/4美元补贴足以保证比例分配且该界是紧的，并将结果扩展到加权情形。
摘要：
我们研究在带补贴（金钱）的情况下，将m个不可分物品公平分配给一组n个智能体的问题。我们的工作主要关注杂务（chores）的分配，但大多数结果也适用于物品（goods）的分配。我们考虑智能体具有（一般的）可加成本函数的情形。假设一个物品对某个智能体造成的最大成本可以用一美元补偿，我们证明总共n/4美元的补贴足以确保一个比例分配。此外，我们证明n/4是紧的，即存在一个包含n个智能体的实例，对于该实例，每个比例分配都需要至少n/4的总补贴。我们还考虑了加权情形，并证明总共(n-1)/2美元的补贴足以确保一个加权比例分配。
英文摘要：
We consider the problem of fair allocation of $m$ indivisible items to a group of $n$ agents with subsidy (money). Our work mainly focuses on the allocation of chores but most of our results extend to the allocation of goods as well. We consider the case when agents have (general) additive cost functions. Assuming that the maximum cost of an item to an agent can be compensated by one dollar, we show that a total of $n/4$ dollars of subsidy suffices to ensure a proportional allocation. Moreover, we show that $n/4$ is tight in the sense that there exists an instance with $n$ agents for which every proportional allocation requires a total subsidy of at least $n/4$. We also consider the weighted case and show that a total subsidy of $(n-1)/2$ suffices to ensure a weighted proportional allocation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
