Proximal Dynamics in Multiagent Network Games

We consider dynamics and protocols for agents seeking an equilibrium in a network game with proximal quadratic cost coupling. We adopt an operator-theoretic perspective to show global convergence to a network equilibrium, under the assumption of convex cost functions with proximal quadratic couplings, time-invariant and time-varying communication graph along with convex local constraints, and a time-invariant communication graph along with convex local constraints and separable convex coupling constraints. We show that proximal dynamics generalize opinion dynamics in social networks and are applicable to distributed tertiary control in power networks.