Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

An asynchronous, forward-backward, distributed generalized Nash equilibrium seeking algorithm

Carlo Cenedese, Giuseppe Belgioioso, Sergio Grammatico, Ming Cao

TL;DR

The work addresses computing a variational generalized Nash equilibrium (v-GNE) for a networked, noncooperative game with affine coupling constraints by introducing an asynchronous, distributed algorithm that operates with node-associated auxiliary variables. It casts the KKT conditions as a monotone inclusion and solves it via a preconditioned forward-backward splitting within an ARock-based asynchronous framework, achieving convergence under bounded delays. The approach preserves scalability as the network grows by using node variables instead of edge variables and proves almost-sure convergence to the unique v-GNE under standard convexity and Lipschitz assumptions. A network Cournot competition demonstrates practical effectiveness, showing robustness to communication delays and improved efficiency due to reduced idle times and flexible update frequencies.

Abstract

In this paper, we propose an asynchronous distributed algorithm for the computation of generalized Nash equilibria in noncooperative games, where the players interact via an undirected communication graph. Specifically, we extend the paper "Asynchronous distributed algorithm for seeking generalized Nash equilibria" by Yi and Pavel: we redesign the asynchronous update rule using auxiliary variables over the nodes rather than over the edges. This key modification renders the algorithm scalable for highly interconnected games. The derived asynchronous algorithm is robust against delays in the communication and it eliminates the idle times between computations, hence modeling a more realistic interaction between players with different update frequencies. We address the problem from an operator-theoretic perspective and design the algorithm via a preconditioned forward-backward splitting. Finally, we numerically simulate the algorithm for the Cournot competition in networked markets.

An asynchronous, forward-backward, distributed generalized Nash equilibrium seeking algorithm

TL;DR

The work addresses computing a variational generalized Nash equilibrium (v-GNE) for a networked, noncooperative game with affine coupling constraints by introducing an asynchronous, distributed algorithm that operates with node-associated auxiliary variables. It casts the KKT conditions as a monotone inclusion and solves it via a preconditioned forward-backward splitting within an ARock-based asynchronous framework, achieving convergence under bounded delays. The approach preserves scalability as the network grows by using node variables instead of edge variables and proves almost-sure convergence to the unique v-GNE under standard convexity and Lipschitz assumptions. A network Cournot competition demonstrates practical effectiveness, showing robustness to communication delays and improved efficiency due to reduced idle times and flexible update frequencies.

Abstract

In this paper, we propose an asynchronous distributed algorithm for the computation of generalized Nash equilibria in noncooperative games, where the players interact via an undirected communication graph. Specifically, we extend the paper "Asynchronous distributed algorithm for seeking generalized Nash equilibria" by Yi and Pavel: we redesign the asynchronous update rule using auxiliary variables over the nodes rather than over the edges. This key modification renders the algorithm scalable for highly interconnected games. The derived asynchronous algorithm is robust against delays in the communication and it eliminates the idle times between computations, hence modeling a more realistic interaction between players with different update frequencies. We address the problem from an operator-theoretic perspective and design the algorithm via a preconditioned forward-backward splitting. Finally, we numerically simulate the algorithm for the Cournot competition in networked markets.

Paper Structure

This paper contains 18 sections, 6 theorems, 35 equations, 2 figures, 3 algorithms.

Table of Contents

  1. INTRODUCTION
  2. Motivation and literature overview
  3. Structure of the paper
  4. NOTATION
  5. Basic notation
  6. Operator-theoretic notation
  7. Problem Formulation
  8. Mathematical formulation
  9. Variational GNE
  10. Synchronous Distributed GNE Seeking
  11. Communication network
  12. Algorithm design
  13. Synchronous, distributed algorithm with node variables (SD-GENO)
  14. Asynchronous Distributed Algorithm
  15. Algorithm design
  16. ...and 3 more sections

Key Result

Proposition 1

Let $\mathcal{A}$ and $\mathcal{B}$ be as in eq:operators_def. Then the following hold:

Figures (2)

  • Figure 1: (a) Interactions of the players $\{1,\dots,8\}$ with the markets $A$, $B$, $C$, $D$, (b) Communication network between players arising from the competition.
  • Figure 2: Communication in alphabetic order (blue) versus random communication (red): (a) Normalized distance from equilibrium,(b) Norm of the disagreement vector, (c) Averaged constraints violation (the negative values are omitted).

Theorems & Definitions (10)

  • Definition 1: Generalized Nash equilibrium
  • Proposition 1
  • Lemma 1
  • Remark 1
  • Theorem 1
  • Remark 2
  • Theorem 2
  • Theorem 3
  • Remark 3
  • Theorem 4