First-Order Algorithms for Constrained Nonlinear Dynamic Games

Abstract: This paper presents algorithms for non-zero sum nonlinear constrained dynamic games with full information. Such problems emerge when multiple players with action constraints and differing objectives interact with the same dynamic system. They model a wide range of applications including economics, defense, and energy systems. We show how to exploit the temporal structure in projected gradient and Douglas-Rachford (DR) splitting methods. The resulting algorithms converge locally to open-loop Nash equilibria (OLNE) at linear rates. Furthermore, we extend stagewise Newton method to find a local feedback policy around an OLNE. In the of linear dynamics and polyhedral constraints, we show that this local feedback controller is an approximated feedback Nash equilibrium (FNE). Numerical examples are provided.