A continuous-time distributed generalized Nash equilibrium seeking algorithm over networks for double-integrator agents

TL;DR

This paper introduces a continuous-time distributed algorithm for double-integrator agents to find generalized Nash equilibria over networks, ensuring convergence under certain mathematical conditions.

Contribution

It develops a fully-distributed dynamic controller based on consensus and primal-dual dynamics, with proven convergence for double-integrator agents in a networked game setting.

Findings

Convergence to variational equilibrium under strong monotonicity.

The proposed controller is fully distributed and relies on local information.

Theoretical guarantees are provided for the stability and convergence of the algorithm.

Abstract

We consider a system of single- or double integrator agents playing a generalized Nash game over a network, in a partial-information scenario. We address the generalized Nash equilibrium seeking problem by designing a fully-distributed dynamic controller, based on continuous-time consensus and primal-dual gradient dynamics. Our main technical contribution is to show convergence of the closed-loop system to a variational equilibrium, under strong monotonicity and Lipschitz continuity of the game mapping, by leveraging monotonicity properties and stability theory for projected dynamical systems.