On the efficiency of Influence-and-Exploit strategies for revenue maximization under positive externalities
Abstract The mitigated effectiveness of traditional forms of advertising along with winner-take-all phenomena caused by globalization and the Internet necessitates a new approach in marketing. Hartline et al. (2008) [16] introduced a marketing model for social networks, where a seller is trying to exploit positive externalities between the buyers and to maximize his revenue by designing an intelligent series of individualized offers. Under this setting, we study the problem of revenue maximization and mostly focus on Influence-and-Exploit (IE) marketing strategies. We show that in undirected social networks, revenue maximization is NP-hard not only when we search for an optimal marketing strategy, but also when we search for the best IE strategy. Rather surprisingly, we observe that allowing IE strategies to offer prices smaller than the myopic price in the exploit step leads to a significant improvement on their performance. Thus, we show that the best IE strategy approximates the maximum revenue within a factor of 0.911 for undirected and of roughly 0.553 for directed social networks. Utilizing a connection between good IE strategies and large cuts in the underlying social network, we obtain polynomial-time algorithms that approximate the revenue of the best IE strategy within a factor of roughly 0.9. Hence, we significantly improve on the best known approximation ratio for revenue maximization to 0.8229 for undirected and to 0.5011 for directed networks (from 2/3 and 1/3, respectively).