SLS-BRD: A system-level approach to seeking generalised feedback Nash equilibria

Abstract

This work proposes a policy learning algorithm for seeking generalised feedback Nash equilibria (GFNE) 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 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.

arXiv comment24 pages, 9 figures; To appear in the IEEE Transactions on Automatic Control, 2025

References in corpus (7)

• A distributed primal-dual algorithm for computation of generalized Nash equilibria with shared affine coupling constraints via operator splitting methods
• Dynamic control of agents playing aggregative games with coupling constraints
• Channel Selection for Network-assisted D2D Communication via No-Regret Bandit Learning with Calibrated Forecasting
• Concurrent learning-based online approximate feedback-Nash equilibrium solution of N-player nonzero-sum differential games
• An Input-Output Parametrization of Stabilizing Controllers: amidst Youla and System Level Synthesis
• The Computation of Approximate Generalized Feedback Nash Equilibria
• Satisficing Paths and Independent Multi-Agent Reinforcement Learning in Stochastic Games