Game-theoretic modeling of vehicle unprotected left turns considering drivers' bounded rationality

Unprotected left turns at signalized intersections represent one of the most critical safety challenges in urban traffic, contributing significantly to severe accidents due to the complex interactions between conflicting vehicles. Given the interactive nature of these conflicts, game theory serves as an ideal framework for modeling vehicle decision-making in unprotected left turns. Although some studies have advanced this by introducing bounded rationality to account for human cognitive limitations, they largely depend on static or heuristic rationality parameters. Such approaches are insufficient to capture the dynamic, interaction-aware evolution of human cognition during complex unprotected left-turn maneuvers. To address this gap, we propose a novel decision-making model for vehicle unprotected left-turn scenarios that integrates game theory with explicit considerations for drivers' dynamic bounded rationality and decision tendency. Our model is formulated as a two-player normal-form game solved by a quantal response equilibrium (QRE), offering a probabilistic depiction of driver decision-making processes that accounts for driving styles and dynamic risk-taking behaviors. We introduce a neural-embedded expectation-maximization (EM)-like alternating optimization framework to calibrate interaction-aware bounded rationality parameters, utilizing high-fidelity microscopic trajectory data for empirical grounding. Simulation experiments demonstrate that the proposed model captures human decision tendencies in high risk scenarios more accurately than perfectly rational models. By quantifying the degree of rationality in critical conflict zones, these findings provide essential insights for developing autonomous driving systems capable of anticipating human error and preventing collisions in mixed traffic environments.