Game-Theoretic Modeling of Vehicle Unprotected Left Turns Considering Drivers' Bounded Rationality

Game-Theoretic Modeling of V ehicle Unprotected Left Turns Considering Drivers' Bounded Rationality Abstract --Modeling the decision-making behavior of vehicles presents unique challenges, particularly during unprotected left turns at intersections, where the uncertainty of human drivers is especially pronounced. In this context, connected autonomous vehicle (CA V) technology emerges as a promising avenue for effectively managing such interactions while ensuring safety and efficiency. Traditional approaches, often grounded in game theory assumptions of perfect rationality, may inadequately capture the complexities of real-world scenarios and drivers' decision-making errors. T o fill this gap, we propose a novel decision-making model for vehicle unprotected left-turn scenarios, integrating game theory with considerations for drivers' bounded rationality. Our model, formulated as a two-player normal-form game solved by a quantal response equilibrium (QRE), offers a more nuanced depiction of driver decision-making processes compared to Nash equilibrium (NE) models. Leveraging an Expectation-Maximization (EM) algorithm coupled with a subtle neural network trained on precise microscopic vehicle trajectory data, we optimize model parameters to accurately reflect drivers' interaction-aware bounded rationality and driving styles. Through comprehensive simulation experiments, we demonstrate the efficacy of our proposed model in capturing the interaction-aware bounded rationality and decision tendencies between players. The proposed model proves to be more realistic and efficient than NE models in unprotected left-turn scenarios. Our findings contribute valuable insights into the vehicle decision-making behaviors with bounded rationality, thereby informing the development of more robust and realistic autonomous driving systems. Connected autonomous vehicle (CA V) refers to a vehicle that can operate autonomously and communicate with other vehicles and infrastructure to enhance safety and efficiency. This work was supported by grants from National Key Research and Development Program of China (2022YFB2503200), Tsinghua University-Mercedes Benz Joint Institute for Sustainable Mobility. Consequently, there arises an urgent need to develop models that enable the operation of CA Vs within mixed traffic environments, enabling them to anticipate the intentions of surrounding human drivers and make human-like decisions based on these expectations and feedback. In the context of mixed traffic environments, one of the most prevalent scenarios entails vehicles executing unprotected left turns at signalized intersections.