  Game-theoretic approaches are envisioned to bring human-like reasoning skills
and decision-making processes for autonomous vehicles (AVs). However,
challenges including game complexity and incomplete information still remain to
be addressed before they can be sufficiently practical for real-world use. Game
complexity refers to the difficulties of solving a multi-player game, which
include solution existence, algorithm convergence, and scalability. To address
these difficulties, a potential game based framework was developed in our
recent work. However, conditions on cost function design need to be enforced to
make the game a potential game. This paper relaxes the conditions and makes the
potential game approach applicable to more general scenarios, even including
the ones that cannot be molded as a potential game. Incomplete information
refers to the ego vehicle's lack of knowledge of other traffic agents' cost
functions. Cost function deviations between the ego vehicle estimated/learned
other agents' cost functions and their actual ones are often inevitable. This
motivates us to study the robustness of a game-theoretic solution. This paper
defines the robustness margin of a game solution as the maximum magnitude of
cost function deviations that can be accommodated in a game without changing
the optimality of the game solution. With this definition, closed-form
robustness margins are derived. Numerical studies using highway lane-changing
scenarios are reported.
