Dissemination and competition between contents in lossy Susceptible Infected Susceptible (SIS) social networks

We model in this work dissemination of contents and competition between sources of contents in social networks composed of a given number of resources (channels or links) used by sources for dissemination of their contents, in the case where some of these resources may be lost during the propagation process, corresponding to the so-called Susceptible Infected Susceptible (SIS) model. We consider two approaches: a static one wherein the source can apply some control, in terms of advertisement for instance, at the start of the dissemination process, and a dynamic one where control can be done at every point in time. We derive, in each case, optimal controls and strategies that maximize the distribution of the contents for linear cost functions, and characterize the Nash equilibrium of the corresponding games: static game for the static optimization case, and differential and stochastic games for the dynamic case, the former when the information on content dissemination is not available at the sources, and the latter when it is.