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

This work proposes a policy learning algorithm for seeking generalized feedback Nash equilibria in $N_{P}$-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 parametrization of their state-feedback policies. Our approach leverages the system level synthesis framework to formulate each player’s update rule as the solution to a robust optimization 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 decentralized control of unstable systems to competition in oligopolistic markets.