Influence of conformist and manipulative behaviors on public opinion

A discrete-time dynamical opinion network is considered in which individuals express their opinions, modeled by scalars, about a certain subject. The reputation (rating) of the subject, herein also referred to as the public opinion, is defined as the arithmetic mean of the expressed opinions. It is assumed that the expressed opinion of an individual may differ from her actual belief due to two main opposing social behaviors, namely, conformity and manipulation. For the purposes of this paper, conformity refers to the tendency of an individual to express an opinion that matches the public opinion, whereas manipulation refers to the tendency of an individual to express an opinion in order to manipulate the public opinion toward her actual belief. The general goal is to investigate how public opinion evolves in the presence of these behaviors via a game-theoretic approach. Several single- and multistage games are introduced to address different relevant scenarios. In all games, the actual beliefs are modeled by scalars in the interval [0,1]. However, the games are organized into two classes, according to the nature of the expressed opinions that represent the players' actions: 1) binary, that is, the action set of each player is the set 0,1, in which case the opinion network resembles a tracking opinion poll, and 2) continuous, that is, the action sets are the interval [0,1], which better captures realistic opinion dynamics in social networks. For each game, the evolution of the subject's reputation as time grows is investigated.