SLS-BRD: A System-Level Approach to Seeking Generalized Feedback Nash Equilibria

This work proposes a policy learning algorithm for seeking generalised feedback Nash equilibria (GFNE) in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{P}$</tex-math></inline-formula>-player noncooperative dynamic games. We consider linear-quadratic games with stochastic dynamics and design a best-response dynamics in which players update and broadcast a parametrisation of their state-feedback policies. Our approach leverages the System Level Synthesis (SLS) framework to formulate each player's update rule as the solution to a robust optimisation problem. Under certain conditions, rates of convergence to a feedback Nash equilibrium can be established. The algorithm is showcased in exemplary problems ranging from the decentralised control of unstable systems to competition in oligopolistic markets.