Abstract
We consider a model of competitive opinion formation in which three persuaders characterized by (possibly unequal) persuasion impacts try to influence opinions in a society of individuals embedded in a social network. Two of the persuaders have the extreme and opposite opinions, and the third one has the centrist opinion. Each persuader chooses one individual to target, i.e., he forms a link with the chosen individual in order to spread his own “point of view” in the society and to get the average long run opinion as close as possible to his own opinion. We examine the opinion convergence and consensus reaching in the society. Also the case when the persuaders choose several targets for diffusion of information is discussed. We study the existence and characterization of pure strategy Nash equilibria in the game played by the persuaders with equal impacts. This characterization depends on influenceability and centrality of the targets. We discuss the effect of the centrist persuader on the consensus and symmetric equilibria, compared to the framework with only two persuaders having the extreme opinions. When the persuasion impacts are unequal with one persuader having a sufficiently large impact, the game has only equilibria in mixed strategies.
Highlights
Social networks play a central role in most of our everyday activities, communicating and exchanging information, sharing knowledge, research and development, advertisement, among many others
The extension of [43] by introducing the third persuader with the centrist opinion has a number of consequences on consensus reaching in the society and Nash equilibria of the noncooperative game played by the persuaders
In this paper we studied a model of competitive opinion formation in a social network
Summary
Social networks play a central role in most of our everyday activities, communicating and exchanging information, sharing knowledge, research and development, advertisement, among many others. We examine the opinion convergence and consensus reaching in the society targeted by the three persuaders. We define a noncooperative game played by the persuaders with strategies being target individuals and study the existence and characterization of pure strategy Nash equilibria. The extension of [43] by introducing the third persuader with the centrist opinion has a number of consequences on consensus reaching in the society and Nash equilibria of the noncooperative game played by the persuaders. Conditions for the existence of symmetric Nash equilibria of the game played by the three equal-impact persuaders is that the relative influence of a potential target must be at least twice higher than the one of any other individual in the network.
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