Some Remarks on Network Games with Local Average

We investigate a class of network games with bounded strategy space, where each player’s action is influenced by her neighbors’ average action. We provide a variational inequality formulation of the model and derive a Katz–Bonacich representation formula for the case where some components of the solution lay on the boundary. Furthermore, we propose algorithms based on the best response dynamics which converge to the unique Nash equilibrium, and study the price of anarchy for a small test problem.