Competition of Influencers: A Model for Maximizing Online Social Impact

The landscape of human interaction has undergone a profound transformation since the advent of Online Social Networks (OSNs). Not only are they changing interpersonal dynamics, but they are also redefining the way businesses, political figures, and media organizations engage with the broader population. In today's digital landscape, OSNs have spawned a new class of social media influencers who play a crucial role in shaping opinion. These influencers actively compete within social media to seize users' attention. Through these targeted efforts, influencers seek to captivate users and build a loyal and engaged fan base, solidifying their position as an authoritative voice in the digital world. In this work, we develop a game-theoretic model for the interactions between users and influencers, where the latter compete to maximize their impact on the population's opinions. The goal of this work is twofold: first, we formalize the problem of maximizing social media impact and study the structure of the optimal solution. Then, taking inspiration from the optimal strategy, we develop a game with two opposing players trying to maximize their influence on users' opinions, for which we characterize the Nash equilibria in pure strategy. The model allows us to evaluate the impact of influencer differences and user population characteristics. In addition, we study the effect of the speed at which user popularity evolves in such a competitive environment. The proposed model proves valuable for brand competition, marketing campaigns, and the ever-evolving political arena.