A semi-dynamic model for competition over popularity and over advertisement space in social networks

Various tools are available for increasing the speed of content dissemination such as embeddinigs in some popular web pages, sharing in some other social networks, and advertisement. In particular, when individuals pass through a content provider to distribute contents, they can benefit from tools such as recommendation systems. The content provider can give a preferential treatment to individuals who pay for advertisement. In this paper we study competition between several contents, each characterized by some given potential popularity. We study competition through advertisements that are placed at the beginning of the dissemination of contents. We answer the question of when is it worthwhile to invest in advertisement as a function of the potential popularity of a content as well as its competing contents. The competition between similar contents (e.g. news channels) over a finite set of potential destinations. We then consider a second model in which there is also competition on advertisement space. We compute the equilibrium strategy and identify its structure and properties for each one of the situations.