On the Efficiency of Influence-and-Exploit Strategies for Revenue Maximization under Positive Externalities
We consider the marketing model of (Hartline, Mirrokni, Sundararajan, WWW ’08) for selling a digital product in a social network under positive externalities. The seller seeks for a marketing strategy, namely an ordering in which he approaches the buyers and the prices offered to them, that maximizes her revenue. We restrict our attention to the Uniform Additive Model of externalities, 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 a general 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 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 the maximum revenue to 0.8229 for undirected and to 0.5011 for directed networks (from 2/3 and 1/3, respectively).
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