Competitive diffusion in signed social networks: A game-theoretic perspective

Abstract

Signed network can be used to effectively characterize both collaborative and antagonistic interactions among individuals in networks. In this paper, we consider a setting in which two stubborn agents compete to maximize the expected number of non-stubborn agents adopting their opinions in a signed network. Here, two stubborn agents hold two competing opinions which never change. They propagate their opinions by selecting some non-stubborn agents (who can change their opinions) to connect to. The payoff of each stubborn agent is denoted by the expected number of non-stubborn agents adopting its opinion. We model the competitive problem as a zero-sum game, where players are the two stubborn agents. Firstly, several properties of this game are presented. Secondly, the signed network with structurally balanced property is investigated, and we find that the number of non-stubborn agents in a subgroup can equal the payoff of one stubborn agent. Moreover, for the signed cycle graph, a necessary and sufficient condition is given to determine whether a strategy profile is Nash equilibrium. Finally, we show that the stubborn agent can increase its payoff by selecting a suitable non-stubborn agent to connect to.