  Dynamic games are an effective paradigm for dealing with the control of
multiple interacting actors. This paper introduces ALGAMES (Augmented
Lagrangian GAME-theoretic Solver), a solver that handles trajectory
optimization problems with multiple actors and general nonlinear state and
input constraints. Its novelty resides in satisfying the first order optimality
conditions with a quasi-Newton root-finding algorithm and rigorously enforcing
constraints using an augmented Lagrangian formulation. We evaluate our solver
in the context of autonomous driving on scenarios with a strong level of
interactions between the vehicles. We assess the robustness of the solver using
Monte Carlo simulations. It is able to reliably solve complex problems like
ramp merging with three vehicles three times faster than a state-of-the-art
DDP-based approach. A model predictive control (MPC) implementation of the
algorithm demonstrates real-time performance on complex autonomous driving
scenarios with an update frequency higher than 60 Hz.
