AI 中文总结
研究m个不可分割物品分给n个代理人的公平分配，在物品效用或负效用受限为1时，证明每人最多补贴一美元可保证无嫉妒分配且界限 tight，还能多项式时间计算，总补贴最多n - 1美元即可。
AI 中文摘要
我们研究了将m个不可分割物品分配给n个具有可加效用的代理人的公平分配问题。在我们的设定中，每个不可分割物品可能是对某些代理人产生非负效用的商品，或是对其他代理人产生负效用的杂务。虽然在不可分割物品设定中可能不存在无嫉妒分配，但引入一定数量的可分割商品（即“钱”）就能实现无嫉妒。当每个物品的效用或负效用被限制在1以内时，我们证明每个代理人最多补贴一美元就足以保证无嫉妒分配的存在，且这个界限是 tight 的。此外，这样的分配可以在多项式时间内计算出来。由于至少有一个代理人无需接受任何补贴，我们的结果意味着最多n - 1美元的总补贴就足以确保无嫉妒。
英文摘要
We study the fair allocation of $m$ indivisible items to $n$ agents with additive utilities. In our setting, each indivisible item may be a good, yielding non-negative utility to some agents, or a chore, yielding negative utility to others. Whilst envy-free allocations may not exist in the indivisible-items setting, envy-freeness can be achieved if some amount of divisible good (i.e., \emph{money}) is introduced. When each item's utility or disutility is bounded by one, we show that a subsidy of at most one dollar per agent suffices to guarantee the existence of an envy-free allocation, and that this bound is tight. Moreover, such an allocation can be computed in polynomial time. Since at least one agent need not receive any subsidy, our results imply that a total subsidy of at most $n-1$ dollars suffices to ensure envy-freeness.
