A new model for product adoption over social networks

Abstract

Building upon the observation that individuals' decisions to purchase a product are influenced by recommendations from their friends as well as their own preferences, in our work, we propose a new model that factors in people's preferences for a product and the number of his/her neighbors that have adopted this product. In our model, as in related ones, beginning with an active seed set (adopters), an adoption action diffuses in a cascade fashion based on a stochastic rule. We demonstrate that under this model, maximizing individuals' adoption of a product, called the product adoption maximization (PAM) problem, is NP-hard, and the objective function for product adoption is sub-modular for time T (T = 1, 2) when the function for estimating the influence coming from neighbors is sub-linear. Hence, a natural greedy algorithm guarantees an approximation. Furthermore, we show that it is hard to approximate the PAM problem when the function for estimating the influence coming from neighbors is not sub-linear. © 2013 Springer-Verlag Berlin Heidelberg.