Game Projection and Robustness for Game-Theoretic Autonomous Driving

Game-theoretic decision making has the potential to bring human-like reasoning skills to autonomous vehicles (AVs), fostering trust between humans and AVs. However, to make these approaches sufficiently practical for real-world use, challenges such as game complexity and incomplete information have to be addressed. Game complexity refers to the difficulties in solving a game-theoretic problem, which include solution existence, algorithm convergence, and scalability. We show in our recent work that a possible solution to overcoming these difficulties is to use potential games. However, constructing a potential game often requires specific cost function designs, limiting their broad use. To address this challenge, we propose to employ a game projection technique in this paper, relaxing the cost function design conditions and making the potential game approach applicable to broader scenarios, even including the ones that cannot be modelled as a potential game. Incomplete information refers to the ego vehicle’s lack of knowledge of other traffic agents’ cost functions. In a driving scenario, deviations of the ego vehicle assumed/estimated others’ cost functions from their actual ones are often inevitable. This necessitate the robustness analysis 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 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.