Modeling and analysis of competitive propagation with social conversion

In this paper we model a class of propagation processes for multiple competing products on a contact network and analyze the resulting dynamical behaviors.We assume three types of product-adoption processes for each individual: self adoption, social adoption and social conversion. On this basis, we build a Markov chain model of the competitive propagation process. Based on the independence approximation, a difference equations system, referred to as the network competitive propagation model, is derived to approximate the original Markov chain. Both simulation work and theoretical results are given to evaluate the accuracy of the independence approximation. The network competitive propagation model does not exclude the long-term coexistence of the mutually exclusive competing products spreading in a single-layer network. The result on coexistence is contrary to some previous literature on the propagation of multiple memes. Moreover, we find that the probability distributions of nodes' states achieve asymptotic consensus, which indicates that our network competitive propagation model is a good example of network dynamics with both consensus and propagation behaviors. Theoretical analysis also reveals that, the rate of convergence to the consensus value depends on the self-adoption process, social conversion process, as well as the network topology.