# Single-timescale distributed GNE seeking for aggregative games over networks via forward-backward operator splitting

## TL;DR

This paper introduces a novel single-timescale distributed algorithm for aggregative games with affine constraints, enabling agents with partial information to reach a variational GNE efficiently through forward-backward operator splitting.

## Contribution

It presents the first single-layer, single-timescale distributed method for variational GNE seeking in aggregative games with affine coupling constraints.

## Key findings

- Algorithm converges under constant step sizes.
- Works with partial information and local communication.
- Utilizes forward-backward splitting for convergence proof.

## Abstract

We consider aggregative games with affine coupling constraints, where agents have partial information on the aggregate value and can only communicate with neighbouring 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., 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.