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 second-order 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. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: X. Di is supported by the National Science Foundation [CAREER Award CMMI-1943998]. E. Iacomini is partially supported by the Italian Research Center on High-Performance Computing, Big Data and Quantum Computing (ICSC) funded by MUR Missione 4-Next Generation EU (NGEU) [Spoke 1 “FutureHPC & BigData”]. C. Segala and M. Herty thank the Deutsche Forschungsgemeinschaft (DFG) for financial support [Grants 320021702/GRK2326, 333849990/IRTG-2379, B04, B05, and B06 of 442047500/SFB1481, HE5386/18-1,19-2,22-1,23-1,25-1, ERS SFDdM035; Germany’s Excellence Strategy EXC-2023 Internet of Production 390621612; and Excellence Strategy of the Federal Government and the Länder]. Support through the EU DATAHYKING is also acknowledged. This work was also funded by the DFG [TRR 154, Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks, Projects C03 and C05, Project No. 239904186]. Moreover, E. Iacomini and C. Segala are members of the Indam GNCS (Italian National Group of Scientific Calculus).