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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.
Lu et al. (Sun,) studied this question.