Game-theoretic decision-making and motion control for connected and automated vehicles in heterogeneous multi-lane merges

Freeway on-ramp merges constitute critical bottlenecks where mandatory lane-changing maneuvers induce severe disruptions within urban traffic systems. While Connected and Automated Vehicles (CAVs) facilitate informed merging, the inevitable transition toward a heterogeneous traffic environment consisting of multi-level intelligent CAVs and human-driven vehicles (HVs) introduces significant coordination challenges. To address this, we propose a game-theoretic microscopic modeling and control strategy for heterogeneous traffic flow at multi-lane merges. By integrating cooperative and non-cooperative game theories with optimal control frameworks, our approach systematically optimizes merging sequences and longitudinal motion trajectories while strictly ensuring safe inter-vehicle spacing. To manage the complex interactions and multiple Nash equilibria inherent in heterogeneous environments, evolutionary game theory is employed to analyze system stability and situation evolution. Numerical and SUMO simulations validate the modeling strategy across varying CAV penetration rates. Results demonstrate that our approach successfully stabilizes the traffic state and significantly mitigates macroscopic queuing. Compared to the full HV baseline where ramp congestion causes severe speed degradation, the proposed algorithm achieves up to a 123.67% increase in average ramp speed at 100% CAV penetration, along with a 17.53% fuel reduction.