<![CDATA[Recently, people became more dependent on online social networks with the increasing use and the rapid development of information technology. Those environments constitute an important area where users interact and create communication ties to maintain their relationships. Furthermore, the time life of these relationships is depending on reputations of the users. Every source (information provider) has a reputation which depends on his frequency of publishing, but also the opinions given by the observers (others users) has an important impact on the determination of this reputation. Since, everyone is trying selfishly to keep a good reputation; a competition is met within these networks. This paper aims to solve this kind of competition through a game theoretic approach; we formulate the said competition as a non-cooperative game, demonstrate the uniqueness of the existent Nash Equilibrium which seems to be the convent solution in this case, then present results clarifying and illustrating the proposed modeling method.]]>
