A Game theoretic approach for competition over visibility in social networks

Social Networks have known an important evolution in the last few years. These structures, made up of individuals who are tied by one or more specific types of interdependency, constitute the window for members to express their opinions and thoughts by sending posts to their own walls or others' timelines. Actually, when a content arrives, it's located on the top of the timeline pushing away older messages. This situation causes a permanent competition over visibility among subscribers who jump on opponents to promote conflict. Our study presents this competition as a non-cooperative game; each source has to choose frequencies which assure its visibility. We model it, exploring the theory of concave games, to reach a situation of equilibrium; a situation where no player has the ultimate ability to deviate from its current strategy. We formulate the named game, then we analyze it and prove that there is exactly one Nash equilibrium which is the convergence of all players' best responses. We finally provide some numerical results, taking into consideration a system of two sources with a specific frequency space, and analyze the effect of different parameters on sources' visibility on the walls of social networks.

[1]  Jorge Martínez-Bauset,et al.  Analysis of price competition under peering and transit agreements in Internet Service provision to peer-to-peer users , 2011, 2011 IEEE Consumer Communications and Networking Conference (CCNC).

[2]  Eitan Altman,et al.  Game theory approach for modeling competition over visibility on social networks , 2014, 2014 Sixth International Conference on Communication Systems and Networks (COMSNETS).

[3]  Eitan Altman,et al.  Telecommunications network equilibrium with price and quality-of-service characteristics , 2003 .

[4]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

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

[6]  Patrick Maillé,et al.  Analysis of Price Competition in a Slotted Resource Allocation Game , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

[7]  Liu Hui.  A Novel QoS Routing Algorithm in Wireless Mesh Networks , 2013 .

[8]  Christos H. Papadimitriou,et al.  Worst-case Equilibria , 1999, STACS.

[9]  Mohsen Tajdinian,et al.  A Secure-Coordinated Expansion Planning of Generation and Transmission Using Game Theory and Minimum Singular Value , 2014 .

[10]  Eitan Altman,et al.  Competition over timeline in social networks , 2013, 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2013).

[11]  Essaid Sabir,et al.  Joint Price and QoS Market Share Game with Adversarial Service Providers and Migrating Customers , 2011, GAMENETS.

[12]  Liu Hui,et al.  A Novel QoS Routing Algorithm in Wireless Mesh Networks , 2013 .

[13]  Sangsoon Lim.  Game-Theoretic Channel Allocation in Cognitive Radio Networks , 2017 .

[14]  Éva Tardos,et al.  Near-optimal network design with selfish agents , 2003, STOC '03.

[15]  Ahmed Habbani,et al.  A Coalition-Formation Game Model for Energy-Efficient Routing in Mobile Ad-hoc Network , 2018 .

[16]  Tim Roughgarden,et al.  How bad is selfish routing? , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

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

[18]  Tim Roughgarden,et al.  Algorithmic Game Theory , 2007 .

[19]  J M Smith,et al.  Evolution and the theory of games , 1976 .