On the efficiency of Influence-and-Exploit strategies for revenue maximization under positive externalities

Abstract

We study the problem of revenue maximization in the marketing model for social networks introduced by (Hartline, Mirrokni, Sundararajan, WWW '08). In this setting, a digital product is sold to a set of potential buyers under positive externalities, and the seller seeks for a marketing strategy, namely an ordering in which he approaches the buyers and the prices offered to them, that maximizes his revenue. We restrict our attention to the Uniform Additive Model and mostly focus on Influence-and-Exploit (IE) marketing strategies. We obtain a comprehensive collection of results on the efficiency and the approximability of IE strategies, which also imply a significant improvement on the best known approximation ratios for revenue maximization. Specifically, we show that in the Uniform Additive Model, both computing the optimal marketing strategy and computing the best IE strategy are NP-hard for undirected social networks. We observe that allowing IE strategies to offer prices smaller than the myopic price in the exploit step leads to a measurable 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. Moreover, we present a natural generalization of IE strategies, with more than two pricing classes, and show that they approximate the maximum revenue within a factor of roughly 0.7 for undirected and of roughly 0.35 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 revenue maximization to 0.8229 for undirected and to 0.5011 for directed networks (from 2/3 and 1/3, respectively, by Hartline et al.).

A monopoly pricing model for diffusion maximization based on heterogeneous nodes and negative network externalities (Case study: A novel product)

“…Here, the challenge is to find a feasible price vector such that node constraints are satisfied and at the same time, total revenue is maximized. Fotakis and Siminelakis (2014) examined the problem of revenue maximization by focusing on IE-strategy. They obtained algorithms with polynomial time that estimate the approximate revenue from the best influence and exploit strategy by an approximate coefficient of 0.9.…”

“…Accordingly, he proposed discriminative pricing strategies, which could be designed based on the type of social relations in order to maximize the profit owned by the provider of communications services. Hartline et al (2008), Mirrokni et al (2012), Fotakis and Siminelakis (2014) and also Arthur et al (2009) analyzed the effect of IE-strategy on revenue gain in addition to proposing algorithms for maximizing the revenue. Hande et al (2010) investigated pricing for internet connection services in the exclusive domain of the ISP (sales of bandwidth to customers) and considered utility of bandwidth consumers which is prone to change in time under the influence of typically unexpected demand.…”

Welfare Maximization with Friends-of-Friends Network Externalities

“…Beside that there is a bunch of work on pricing strategies for selling an item in social networks that exploit 1-hop network externalities to maximize the revenue of a seller [1,5,10,16,21,28], most prominent the work of Hartline et al [21]. In these settings one typically first sells products for a discount to some customers to later exploit their positive influence on the other customers to maximize revenue.…”

“…Inequality (15) follows from the nonnegativity of f i,j (.). For Inequality (16) observe that for any fixed i ∈ I it holds that j ∈V f i,j (n) ≤ j ∈V f i * ,j (n) by the definition of i * . Further, j ∈V f i * ,j (n) does not depend on i, which implies the left-hand side of Equality (17).…”

“…There is a large body of work on mechanisms and pricing strategies for this problem with a single [1,3,5,6,9,10,16,19,21,28] or multiple items [2,7,12,18,24,[30][31][32] when the valuation function of a user depends solely on the 1-hop neighborhood of a user and the user itself. All this work assumes that there is an infinite supply of items (of each type if there are different items) and the users have unit-demand, that is, they want to buy only one item.…”