Distributed Computation of Stochastic GNE with Partial Information: An Augmented Best-Response Approach

TL;DR

This paper introduces a distributed algorithm for solving stochastic generalized Nash equilibrium problems under partial information, utilizing an augmented best-response approach with convergence guarantees and practical numerical demonstrations.

Contribution

It proposes a novel distributed stochastic GNE seeking algorithm based on Douglas-Rachford splitting that relaxes previous assumptions and handles partial decision information.

Findings

Converges to a true Nash equilibrium under stochastic and partial information settings.

Effectively solves large-scale stochastic GNE problems with numerical examples.

Uses an augmented best-response scheme with inexact subproblem solutions.

Abstract

In this paper, we focus on the stochastic generalized Nash equilibrium problem (SGNEP) which is an important and widely-used model in many different fields. In this model, subject to certain global resource constraints, a set of self-interested players aim to optimize their local objectives that depend on their own decisions and the decisions of others and are influenced by some random factors. We propose a distributed stochastic generalized Nash equilibrium seeking algorithm in a partial-decision information setting based on the Douglas-Rachford operator splitting scheme, which relaxes assumptions in the existing literature. The proposed algorithm updates players' local decisions through augmented best-response schemes and subsequent projections onto the local feasible sets, which occupy most of the computational workload. The projected stochastic subgradient method is applied to provide approximate solutions to the augmented best-response subproblems for each player. The Robbins-Siegmund theorem is leveraged to establish the main convergence results to a true Nash equilibrium using the proposed inexact solver. Finally, we illustrate the validity of the proposed algorithm via two numerical examples, i.e., a stochastic Nash-Cournot distribution game and a multi-product assembly problem with the two-stage model.