A Stochastic Game Approach for Competition over Popularity in Social Networks

The global Internet has enabled a massive access of internauts to content. At the same time, it allowed individuals to use the Internet in order to distribute content. When individuals pass through a content provider to distribute contents, they can benefit from many tools that the content provider has in order to accelerate the dessimination of the content. These include caching as well as recommendation systems. The content provider gives 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 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, who are faced with a similar question. We formulate the problem as a stochastic game with a finite state and action space and obtain the structure of the equilibria policy under a linear structure of the dissemination utility as well as on the advertisement costs. We then consider open loop control (no state information) and solve the game using a transformation into a differential game with a compact state space.