Diversified-profit maximization in competitive social advertising

Due to the important role that social networks play in advertisements and propaganda, influence maximization (IM) problem which aims at finding some influential users as seeds to trigger large online cascading influence spread has been a hot research topic in the past two decades. As an extension of classical IM problem, profit maximization (PM) problem is inspired by product promotion and focuses on the profit generated by consumer. Given that competitive social advertising is more common in real-world, a series of studies propose some versions of PM problem. However, the competition happening in the information dissemination of imperfect substitutes and the influence of potential consumers' preference have been mostly ignored. Besides, to the best of our knowledge, no research pays attention on the fact that some companies may snatch seeds to limit the profits of their opponents. Therefore, we propose a novel competition-based diversified-profit maximization (CDM) problem and its adaptive version, i.e., adaptive competition-based diversified-profit maximization (ACDM) problem. Different from prior works, these problems take seed's preference into consideration and use social welfare to reflect it. These two problems aim at selecting seeds and allocating them to marketers such that the sum of profit generated by consumers for a special entity after information dissemination and social welfare with respect to seed allocation reaches maximum. To address these two problems, we design an algorithm which combines the method of online allocation and the concept of Shapley value. Experimental results on three real-world data sets demonstrate the effectiveness of our proposed algorithm.