We consider the problem of allocating multiple indivisible items to a set of networked agents to maximize the social welfare subject to network externalities. Here, the social welfare is given by the sum of agents' utilities and externalities capture the effect that one user of an item has on the item's value to others. We first provide a general formulation that captures some of the existing models as a special case. We then show that the social welfare maximization problem benefits some nice diminishing or increasing marginal return properties. That allows us to devise polynomial-time approximation algorithms using the Lovasz extension and multilinear extension of the objective functions. Our principled approach recovers or improves some of the existing algorithms and provides a simple and unifying framework for maximizing social welfare subject to network externalities.

翻译：我们考虑了在存在网络外部性的情况下，将多个不可分割物品分配给一组网络化智能体以最大化社会福利的问题。此处的社会福利由各智能体效用之和给出，而外部性则刻画了某一物品的一个使用者对该物品在其他使用者眼中价值的影响。首先，我们提出一个通用框架，其将部分现有模型作为特例予以囊括。进而，我们证明社会福利最大化问题具有某些理想的边际收益递减或递增性质。这使得我们能够利用目标函数的Lovász拓展和多线性拓展来设计多项式时间近似算法。我们的原则性方法复原或改进了部分现有算法，并为在存在网络外部性情况下最大化社会福利提供了一个简单统一的框架。