Influence propagation in adversarial setting

Abstract

It has been observed that individuals' decisions to adopt a product or innovation are often influenced by the recommendations of their friends and acquaintances. Motivated by this observation, the last few years have seen a number of studies on influence maximization in social networks. The primary goal of these studies is identification of k most influential nodes in a network. A major limitation of these studies is that they focus on a non-adversarial environment, where only one player is engaged in influencing the nodes. However, in a realistic scenario multiple players attempt to influence the nodes in a competitive fashion. The proposed model considers a competitive environment where a node that has not yet adopted an innovation, can adopt only one of the several competing innovations and once it adopts an innovation, it does not switch. The paper studies the scenario where the first player has already chosen a set of k nodes and the second player, with the knowledge of the choice of the first, attempts to identify a smallest set of nodes (excluding the ones already chosen by the first) so that when the influence propagation process ends, the number of nodes influenced by the second player is larger than the number of nodes influenced by the first.