Nash Equilibrium in Social Media

In this work, we investigate an application of a Nash equilibrium seeking algorithm in a social network. In a networked game each player (user) takes action in response to other players' actions in order to decrease (increase) his cost (profit) in the network. We assume that the players' cost functions are not necessarily dependent on the actions of all players. This is due to better mimicking the standard social media rules. A communication graph is defined for the game through which players are able to share their information with only their neighbors. We assume that the communication neighbors necessarily affect the players' cost functions while the reverse is not always true. In this game, the players are only aware of their own cost functions and actions. Thus, each of them maintains an estimate of the others' actions and share it with the neighbors to update his action and estimates.