A Note on Generalized Nash Games Played on Networks

We investigate a generalized Nash equilibrium problem where players are modeled as nodes of a network and the utility function of each player depends on his/her own action as well as on the actions of his/her neighbors in the network. In the case of a quadratic reference model with shared constraints we are able to derive the variational solution of the game as a series expansion which involves the powers of the adjacency matrix, thus extending a previous result. Our analysis is illustrated by means of some numerical examples.