A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games

TL;DR

This paper introduces a semi-decentralized Douglas-Rachford splitting algorithm for finding equilibria in generalized aggregative games with affine constraints, demonstrating faster convergence than existing methods.

Contribution

The paper develops a novel Douglas-Rachford based algorithm for equilibrium seeking in aggregative games, with proven convergence and improved speed.

Findings

Faster convergence compared to forward-backward algorithms

Global convergence guaranteed under mild assumptions

Effective in resource allocation game scenarios

Abstract

We address the generalized aggregative equilibrium seeking problem for noncooperative agents playing average aggregative games with affine coupling constraints. First, we use operator theory to characterize the generalized aggregative equilibria of the game as the zeros of a monotone set-valued operator. Then, we massage the Douglas-Rachford splitting to solve the monotone inclusion problem and derive a single layer, semi-decentralized algorithm whose global convergence is guaranteed under mild assumptions. The potential of the proposed Douglas-Rachford algorithm is shown on a simplified resource allocation game, where we observe faster convergence with respect to forward-backward algorithms.