Distributed GNE seeking over networks in aggregative games with coupled constraints via forward-backward operator splitting

We consider the framework of aggregative games with affine coupling constraints, where agents have partial information of the aggregate value of the population and can only obtain information from neighbouring agents. We propose a single-layer, distributed algorithm that reaches the variational Generalized Nash Equilibrium, under constant step sizes. Additionally, the algorithm works on a single timescale, i.e., doesn't require multiple communication rounds between agents before updating their action. The convergence proof leverages an invariance property of the aggregate estimates and relies on a forward-backward splitting for two preconditioned operators and their restricted (strong) monotonicity properties on the consensus subspace.