We study a revenue maximization problem in the context of social networks. Namely, we generalize a model introduced by Alon, Mansour, and Tennenholtz [2] that captures inequity aversion, i.e., it captures the fact that prices offered to neighboring nodes should not differ significantly. We first provide approximation algorithms for a natural class of instances, where the total revenue is the sum of single-value revenue functions. Our results improve on the current state of the art, especially when the number of distinct prices is small. This applies, for instance, to settings where the seller will only consider a fixed number of discount types or special offers. To complement our positive results, we resolve one of the open questions posed in [2] by establishing APX-hardness for the problem. Surprisingly, we further show that the problem is NP-complete even when the price differences are allowed to be large, or even when the number of allowed distinct prices is as small as three. Finally, we study extensions of the model regarding the demand type of the clients.

我们研究了社交网络中的收益最大化问题。也就是说，我们推广了由Alon，Mansour和Tennenholtz [2]引入的模型，该模型捕获了不平等厌恶，即捕获了提供给相邻节点的价格不应有显着差异的事实。我们首先为自然实例类别提供近似算法，其中总收入是单值收入函数的总和。我们的结果在当前的技术水平上得到了改善，尤其是当不同价格的数量很少时。例如，这适用于卖方仅考虑固定数量的折扣类型或特惠的设置。为了补充我们的积极成果，我们通过建立问题的APX硬度来解决[2]中提出的一个开放性问题。出人意料的是，我们进一步表明，即使允许价格差异较大，甚至允许的不同价格数量只有三个，问题仍然是NP完全问题。最后，我们研究有关客户需求类型的模型扩展。