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.

[1]  Rui Wang,et al.  A Review of Microblogging Marketing Based on the Complex Network Theory , 2011, 2011 International Conference in Electrics, Communication and Automatic Control Proceedings.

[2]  P. Brémaud.  Point processes and queues, martingale dynamics , 1983 .

[3]  Esko Valkeila,et al.  An Introduction to the Theory of Point Processes, Volume II: General Theory and Structure, 2nd Edition by Daryl J. Daley, David Vere‐Jones , 2008 .

[4]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[5]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

[6]  Jennifer Wortman,et al.  Viral Marketing and the Diffusion of Trends on Social Networks , 2008 .

[7]  P. Brémaud.  Point Processes and Queues , 1981 .

[8]  E. Altman.  Constrained Markov Decision Processes , 1999 .

[9]  Daryl J. Daley,et al.  An Introduction to the Theory of Point Processes , 2013 .

[10]  Jeffrey D. Scargle,et al.  An Introduction to the Theory of Point Processes, Vol. I: Elementary Theory and Methods , 2004, Technometrics.

[11]  Eitan Altman.  A Stochastic Game Approach for Competition over Popularity in Social Networks , 2013, Dyn. Games Appl..

[12]  P. Bremaud,et al.  Point Processes and Queues: Martingale Dynamics (Springer Series in Statistics) , 1981 .

[13]  Eitan Altman,et al.  An epidemic game between contents in a wireless network , 2012, 2012 International Symposium on Wireless Communication Systems (ISWCS).

[14]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[15]  Eitan Altman.  Game theoretic approaches for studying competition over popularity and over advertisement space in social networks , 2012 .

[16]  Klaus Wälde,et al.  “Itô's Lemma” and the Bellman Equation for Poisson Processes: An Applied View , 2006 .

[17]  T. Başar,et al.  Dynamic Noncooperative Game Theory, 2nd Edition , 1998 .