Network aggregative games: distributed covergence to Nash equilibria

We consider quasi-aggregative games for large populations of heterogeneous agents, whose interaction is determined by an underlying communication network. Specifically, each agent minimizes a quadratic cost function, which depends on its own strategy and on a convex combination of the strategies of its neighbors, and is subject to heterogeneous convex constraints. We suggest two distributed algorithms that can be implemented to steer the best responses of the rational agents to a Nash equilibrium configuration. The convergence of these schemes is guaranteed under different sufficient conditions depending on the matrices defining the agents' cost functions and on the communication network.