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We consider aggregative games with affine coupling constraints, where agents have partial information on the aggregate value and can only communicate with neighboring agents. We propose a single-layer distributed algorithm that reaches a variational generalized Nash equilibrium, under constant step sizes. The algorithm works on a single timescale, i.e., it does not 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.

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