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

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.