A continuous-time distributed generalized Nash equilibrium seeking algorithm over networks for double-integrator agents

We consider a system of single- or double-integrator agents playing a generalized Nash game over a network, in a partial-information scenario. We address the generalized Nash equilibrium seeking problem by designing a fully-distributed dynamic controller, based on continuous-time consensus and primal-dual gradient dynamics. Our main technical contribution is to show convergence of the closed-loop system to a variational equilibrium, under strong monotonicity and Lipschitz continuity of the game mapping, by leveraging monotonicity properties and stability theory for projected dynamical systems.