ABSTRACT We consider a monopolistic, biased news media platform that attempts to influence the decision of swing voters with cheap talk when voting is costly and abstaining is an option. First, we demonstrate that, while no fully communicative equilibrium exists in a stage game, a partially truth‐revealing mixed‐strategy equilibrium exists. We also characterize the equilibria in infinitely repeated games in which the news media's information distortion is monitored ex post after voting, resulting in the swing voter's transitioning to the punishment phase with positive probability. Notably, under perfect monitoring, repeated interactions do not reduce the news media's steering probability, whereas they do reduce the likelihood of the swing voter's abstention. Under imperfect monitoring, a voter's cheap talk as well as the media's cheap talk can help construct a partially communicative equilibrium. In both perfect and imperfect monitoring cases, a mixed‐strategy equilibrium can enhance efficiency even though media bias persists, akin to what is observed in a stage game, providing a probable explanation for the persistence of biased news media.
Jun et al. (Wed,) studied this question.