论不可分割物的公平分割
On Fair Division of Indivisible Items
摘要：
我们考虑以公平的方式将不可分割的货物分配给一组代理人的任务。我们的公平概念是纳什社会福利，即，目标是最大化代理效用的几何平均值。每种商品都有多个物品或副本，当代理人收到更多相同商品的物品时，其效用就会减少。对于一个代理人来说，一组项目的效用是该组中项目的效用之和。每个代理人都有一个效用上限，超过这个上限，他就不会对额外的物品进行估值。我们给出了一个多项式时间近似算法，最大限度地提高纳什社会福利的一个因素的$e^{1/{e}} \approx 1.445$。计算出的分配是帕累托最优的，并且近似于一个项目的无嫉妒度，最多为$2 + \eps$的因子
英文摘要：
We consider the task of assigning indivisible goods to a set of agents in a fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is to maximize the geometric mean of the utilities of the agents. Each good comes in multiple items or copies, and the utility of an agent diminishes as it receives more items of the same good. The utility of a bundle of items for an agent is the sum of the utilities of the items in the bundle. Each agent has a utility cap beyond which he does not value additional items. We give a polynomial time approximation algorithm that maximizes Nash social welfare up to a factor of $e^{1/{e}} \approx 1.445$. The computed allocation is Pareto-optimal and approximates envy-freeness up to one item up to a factor of $2 + \eps$
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。
