Game theory approach for modeling competition over visibility on social networks

In Social Networks, such as facebook, linkedin, twitter, google+ and others, many members post messages to walls or to timelines of their friends, or to that of pages or of groups. There is permanent competition over visibility of content in these destination since timelines have finite capacity. As new content arrives, older content gets pushed away from the timeline. A selfish source that wishes to be more visible has to send from time to time new content thus preempting other content from the time-line. We assume that sending more content comes with some extra cost. We analyse the problem of selecting the rates of content creation as a non-cooperative game between several sources that share some common destination to which they send content. We identify conditions under which the problem can be reduced to the Kelly mechanism for which we compute explicitly the equilibrium. This is done in a very general probabilistic framework where time between arrival of content is only required to be stationary ergodic.