The bang for the buck

Abstract

The key algorithmic problem in viral marketing is to identify a set of influential users (called seeds) in a social network, who, when convinced to adopt a product, shall influence other users in the network, leading to a large number of adoptions. When two or more players compete with similar products on the same network we talk about competitive viral marketing, which so far has been studied exclusively from the perspective of one of the competing players. In this paper we propose and study the novel problem of competitive viral marketing from the perspective of the host, i.e., the owner of the social network platform. The host sells viral marketing campaigns as a service to its customers, keeping control of the selection of seeds. Each company specifies its budget and the host allocates the seeds accordingly. From the host's perspective, it is important not only to choose the seeds to maximize the collective expected spread, but also to assign seeds to companies so that it guarantees the bang for the buck for all companies is nearly identical, which we formalize as the fair seed allocation problem. We propose a new propagation model capturing the competitive nature of viral marketing. Our model is intuitive and retains the desired properties of monotonicity and submodularity. We show that the fair seed allocation problem is NP-hard, and develop an efficient algorithm called Needy Greedy. We run experiments on three real-world social networks, showing that our algorithm is effective and scalable.