Abstract
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.
Highlights
We study a differential pricing optimization problem in the presence of network effects
We are interested in studying differential pricing in the context of a social network
A second example of negative externalities, which is the focus of our work, and arises from differential pricing, is inequity aversion, see e.g., [4] and [8]
Summary
We study a differential pricing optimization problem in the presence of network effects. A second example of negative externalities, which is the focus of our work, and arises from differential pricing, is inequity aversion, see e.g., [4] and [8]. This means that a customer may experience dissatisfaction if she realizes that other people within her social circle, were offered a better deal for the same service. The seller is allowed to not make a price offer to some nodes (referred to as introducing discontinuities, see the related discussion in Section 2), in which case the difference constraints do not apply for the edges incident to these nodes. Other types of negative externalities have been considered e.g., in [3, 5] which study the effects of invidious consumption
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