A Game theoretic approach for competition over visibility in social networks

Social Networks have known an important evolution in the last few years. These structures, made up of individuals who are tied by one or more specific types of interdependency, constitute the window for members to express their opinions and thoughts by sending posts to their own walls or others' timelines. Actually, when a content arrives, it's located on the top of the timeline pushing away older messages. This situation causes a permanent competition over visibility among subscribers who jump on opponents to promote conflict. Our study presents this competition as a non-cooperative game; each source has to choose frequencies which assure its visibility. We model it, exploring the theory of concave games, to reach a situation of equilibrium; a situation where no player has the ultimate ability to deviate from its current strategy. We formulate the named game, then we analyze it and prove that there is exactly one Nash equilibrium which is the convergence of all players' best responses. We finally provide some numerical results, taking into consideration a system of two sources with a specific frequency space, and analyze the effect of different parameters on sources' visibility on the walls of social networks.