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In this paper, we investigate the discount allocation problem in socialnetworks. It has been reported that 40\% of consumers will share an email offerwith their friend and 28\% of consumers will share deals via social mediaplatforms. What does this mean for a business? Essentially discounts should notjust 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 theinfluence maximization discount allocation problem: given a social network andbudget, we need to decide to which initial set users should offer thediscounts, and how much should the discounts be worth. Our goal is to maximizethe number of customers who finally adopt the target product. We investigatethis problem under both non-adaptive and adaptive settings. In the firstsetting, we have to commit the set of seed users and corresponding discountsall at once in advance. In the latter case, the decision process is performedin a sequential manner, and each seed user that is picked provides the feedbackon the discount, or, in other words, reveals whether or not she will adopt thediscount. We propose a simple greedy policy with an approximation ratio of$\frac{1}{2}(1 - 1/e)$ in non-adaptive setting. For the significantly morecomplex adaptive setting, we propose an adaptive greedy policy with boundedapproximation ratio in terms of expected utility.

Going viral: Optimizing Discount Allocation in Social Networks for Influence Maximization