Lie-Bracket Nash Equilibrium Seeking with Bounded Update Rates for Noncooperative Games

TL;DR

This paper introduces a model-free, distributed extremum seeking control method using Lie-brackets for local convergence to Nash equilibrium in quadratic noncooperative games, with stability analysis and numerical validation.

Contribution

It is the first to combine noncooperative game solving with extremum seeking and bounded update rates in a model-free framework.

Findings

Proves local convergence to Nash equilibrium.

Quantifies residual set size around equilibrium.

Validates results through numerical example.

Abstract

This paper proposes a novel approach for local convergence to Nash equilibrium in quadratic noncooperative games based on a distributed Lie-bracket extremum seeking control scheme. This is the first instance of noncooperative games being tackled in a model-free fashion integrated with the extremum seeking method of bounded update rates. In particular, the stability analysis is carried out using Lie-bracket approximation and Lyapunov's direct method. We quantify the size of the ultimate small residual sets around the Nash equilibrium and illustrate the theoretical results numerically on an example in an oligopoly setting.