Going viral: Optimizing Discount Allocation in Social Networks for   Influence Maximization
  In this paper, we investigate the discount allocation problem in social networks. It has been reported that 40\% of consumers will share an email offer with their friend and 28\% of consumers will share deals via social media platforms. What does this mean for a business? Essentially discounts should not just be treated as short term solutions to attract individual customer, instead, allocating discounts to a small fraction of users (called seed users) may trigger a large cascade in a social network. This motivates us to study the influence maximization discount allocation problem: given a social network and budget, we need to decide to which initial set users should offer the discounts, and how much should the discounts be worth. Our goal is to maximize the number of customers who finally adopt the target product. We investigate this problem under both non-adaptive and adaptive settings. In the first setting, we have to commit the set of seed users and corresponding discounts all at once in advance. In the latter case, the decision process is performed in a sequential manner, and each seed user that is picked provides the feedback on the discount, or, in other words, reveals whether or not she will adopt the discount. We propose a simple greedy policy with an approximation ratio of $\frac{1}{2}(1 - 1/e)$ in non-adaptive setting. For the significantly more complex adaptive setting, we propose an adaptive greedy policy with bounded approximation ratio in terms of expected utility. 
Shaojie Tang and Jing Yuan
cs.SI cs.GT