Word of Mouth: Rumor Dissemination in Social Networks

In this paper we examine the diffusion of competing rumors in social networks. Two players select a disjoint subset of nodes as initiators of the rumor propagation, seeking to maximize the number of persuaded nodes. We use concepts of game theory and location theory and model the selection of starting nodes for the rumors as a strategic game. We show that computing the optimal strategy for both the first and the second player is NP-complete, even in a most restricted model. Moreover we prove that determining an approximate solution for the first player is NP-complete as well. We analyze several heuristics and show that--counter-intuitively--being the first to decide is not always an advantage, namely there exist networks where the second player can convince more nodes than the first, regardless of the first player's decision.