Nash Equilibrium in Social Media
For researchers in distributed optimization and game theory, this provides a theoretical framework for decentralized decision-making in social networks, though the contribution is incremental.
This work applies a Nash equilibrium seeking algorithm to social networks, where players' cost functions depend only on neighbors' actions, and players estimate others' actions via local communication. The algorithm converges to Nash equilibrium under the proposed game model.
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.