Pricing strategies for viral marketing on Social Networks

We study the use of viral marketing strategies on social networks to maximize revenue from the sale of a single product. We propose a model in which the decision of a buyer to buy the product is influenced by friends that own the product and the price at which the product is offered. The influence model we analyze is quite general, naturally extending both the Linear Threshold model and the Independent Cascade model, while also incorporating price information. We consider sales proceeding in a cascading manner through the network, i.e. a buyer is offered the product via recommendations from its neighbors who own the product. In this setting, the seller influences events by offering a cashback to recommenders and by setting prices (via coupons or discounts) for each buyer in the social network. Finding a seller strategy which maximizes the expected revenue in this setting turns out to be NP-hard. However, we propose a seller strategy that generates revenue guaranteed to be within a constant factor of the optimal strategy in a wide variety of models. The strategy is based on an influence-and-exploit idea, and it consists of finding the right trade-off at each time step between: generating revenue from the current user versus offering the product for free and using the influence generated from this sale later in the process. We also show how local search can be used to improve the performance of this technique in practice.

💡 Research Summary

The paper investigates how a seller can maximize revenue when a single product spreads virally through a social network. The authors extend classic diffusion models—Linear Threshold (LT) and Independent Cascade (IC)—by incorporating price sensitivity. In their model each user i has a purchase probability that depends on two factors: the number k_i of neighbors who already own the product (social influence) and the price p_i offered to the user. Formally the probability is expressed as f_i(p_i, k_i) = g_i(k_i)·h_i(p_i), where g_i captures the increasing effect of recommendations and h_i captures the decreasing effect of higher prices. Both functions are assumed monotone, which allows analytical tractability while still being expressive enough to model realistic behavior.

Sales proceed in a cascading fashion. The seller first selects a seed set S and decides whether to give those users the product for free, at a discount, or at a regular price. When a user purchases, she may recommend the product to her neighbors. The seller can influence this process in two ways: (1) by offering a cash‑back reward r_i to any user who successfully recommends the product (an incentive for further diffusion) and (2) by setting an individualized price p_i (or coupon) for each user. The expected revenue is therefore

R = ∑_i (p_i − r_i)·Pr