Inequity Aversion Pricing over Social Networks: Approximation Algorithms and Hardness Results

TL;DR

This paper investigates revenue maximization in social networks considering inequity aversion, providing approximation algorithms for specific cases and establishing hardness results, including NP-completeness and APX-hardness, with extensions to the model.

Contribution

It introduces improved approximation algorithms for single-value revenue functions and resolves open questions by proving NP-completeness and APX-hardness in various settings.

Findings

Approximation algorithms outperform previous methods for small number of prices.

NP-completeness holds even with large price differences or only three prices.

The problem is APX-hard, indicating difficulty in approximation.

Abstract

We study a revenue maximization problem in the context of social networks. Namely, we consider a model introduced by Alon, Mansour, and Tennenholtz (EC 2013) that captures inequity aversion, i.e., prices offered to neighboring vertices should not be significantly different. We first provide approximation algorithms for a natural class of instances, referred to as the class 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 example, to settings where the seller will only consider a fixed number of discount types or special offers. We then resolve one of the open questions posed in Alon et al., 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 provide some extensions of the model, regarding either the allowed set of prices or the demand type of the clients.