Single-Timescale Distributed GNE Seeking for Aggregative Games Over Networks via Forward–Backward Operator Splitting

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