Distributed GNE seeking under partial-decision information over networks via a doubly-augmented operator splitting approach

TL;DR

This paper proposes a fully distributed algorithm for computing generalized Nash equilibria in networked games with shared constraints, using a doubly-augmented operator splitting approach under partial-decision information.

Contribution

It introduces a novel single-layer distributed algorithm that handles partial information and converges to a variational GNE via primal-dual operator splitting.

Findings

Algorithm converges to a variational GNE with fixed step-sizes.

Operates under partial-decision information and arbitrary network topology.

Utilizes a doubly-augmented operator splitting framework.

Abstract

We consider distributed computation of generalized Nash equilibrium (GNE) over networks, in games with shared coupling constraints. Existing methods require that each player has full access to opponents' decisions. In this paper, we assume that players have only partial-decision information, and can communicate with their neighbours over an arbitrary undirected graph. We recast the problem as that of finding a zero of a sum of monotone operators through primal-dual analysis. To distribute the problem, we doubly augment variables, so that each player has local decision estimates and local copies of Lagrangian multipliers. We introduce a single-layer algorithm, fully distributed with respect to both primal and dual variables. We show its convergence to a variational GNE with fixed step-sizes, by reformulating it as a forward-backward iteration for a pair of doubly-augmented monotone operators.