We consider the problem of maximizing social welfare by allocating indivisible items to a set of agents subject to network externalities. We first provide a general formulation that captures some of the known models as a special case. We then show that the social welfare maximization problem benefits some nice sub-or supermodular properties. That allows us to devise simple polynomial-time approximation algorithms using Lov\'asz extension and multilinear extension of the objective function. Our principled approach recovers or improves some of the existing algorithms and provides a simple unifying method for maximizing social welfare subject to network externalities.

中文翻译：

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受网络外部性影响最大的社会福利：统一的子模块优化方法

我们考虑通过将不可分割的项目分配给受网络外部性影响的一组代理来最大化社会福利的问题。我们首先提供一个概括性的表述，其中包含一些已知模型的特殊情况。然后，我们证明了社会福利最大化问题有益于一些很好的次模量或超模量性质。这使我们能够使用目标函数的Lov'asz扩展和多线性扩展来设计简单的多项式时间近似算法。我们的原则性方法可以恢复或改进某些现有算法，并提供一种简单的统一方法来最大化受网络外部性影响的社会福利。