A Game-Theoretic Framework for Generic Second-Order Traffic Flow Models Using Mean Field Games and Adversarial Inverse Reinforcement Learning

A traffic system can be interpreted as a multiagent system, wherein vehicles choose the most efficient driving approaches guided by interconnected goals or strategies. This paper aims to develop a family of mean field games (MFG) for generic second-order traffic flow models (GSOM), in which cars control individual velocity to optimize their objective functions. GSOMs do not generally assume that cars optimize self-interested objectives, so such a game-theoretic reinterpretation offers insights into the agents' underlying behaviors. In general, an MFG allows one to model individuals on a microscopic level as rational utility-optimizing agents while translating rich microscopic behaviors to macroscopic models. Building on the MFG framework, we devise a new class of secondorder traffic flow MFGs (i.e., GSOM-MFG), which control cars' acceleration to ensure smooth velocity change. A fixed-point algorithm with fictitious play technique is developed to solve GSOM-MFG numerically. In numerical examples, different traffic patterns are presented under different cost functions. For real-world validation, we further use an inverse reinforcement learning approach (IRL) to uncover the underlying cost function on the next-generation simulation (NGSIM) data set. We formulate the problem of inferring cost functions as a min-max game and use an apprenticeship learning algorithm to solve for cost function coefficients. The results show that our proposed GSOM-MFG is a generic framework that can accommodate various cost functions. The Aw Rascle and Zhang (ARZ) and Light-Whitham-Richards (LWR) fundamental diagrams in traffic flow models belong to our GSOM-MFG when costs are specified.