  Trajectory planning for autonomous race cars poses special challenges due to
the highly interactive and competitive environment. Prior work has applied game
theory as it provides equilibria for such non-cooperative dynamic problems.
This contribution introduces a framework to assess the suitability of the Nash
equilibrium for racing scenarios. To achieve this, we employ a variant of iLQR,
called iLQGame, to find trajectories that satisfy the equilibrium conditions
for a linear-quadratic approximation of the original game. In particular, we
are interested in the difference between the behavioral outcomes of the
open-loop and the feedback Nash equilibria and show how iLQGame can generate
both types of equilibria. We provide an overview of open problems and upcoming
research, including convergence properties of iLQGame in racing games, cost
function parameterization, and moving horizon implementations.
