  Interaction-aware trajectory planning is crucial for closing the gap between
autonomous racing cars and human racing drivers. Prior work has applied game
theory as it provides equilibrium concepts for non-cooperative dynamic
problems. With this contribution, we formulate racing as a dynamic game and
employ a variant of iLQR, called iLQGames, to solve the game. iLQGames finds
trajectories for all players that satisfy the equilibrium conditions for a
linear-quadratic approximation of the game and has been previously applied in
traffic scenarios. We analyze the algorithm's applicability for trajectory
planning in racing scenarios and evaluate it based on interaction awareness,
competitiveness, and safety. With the ability of iLQGames to solve for
open-loop and feedback Nash equilibria, we compare the behavioral outcomes of
the two equilibrium concepts in simple scenarios on a straight track section.
