Risk appetite-enhanced game-theoretic approach for modelling mandatory lane-changing behaviour in freeway merging areas

Addressing adverse effects on traffic safety resulting from mandatory lane changes presents a significant challenge, necessitating the development of an empirically accurate method that incorporates drivers’ risk appetite into modelling merging behaviour. Game theory serves as a commonly utilized approach for analysing interactive lane-changing behaviour and accurately predicting various vehicle actions. This study introduces a game-theoretical decision-making model tailored for mandatory lane changes at freeway merging areas. The proposed model adopts a non-cooperative decision-making approach involving two players: the driver of the mainline vehicle and the on-ramp vehicle. The payoff function, encompassing both efficiency-based and safety-based payoffs, is asymmetrically designed to evaluate safety loss and efficiency gain, adhering to the principles of prospect theory. Specifically, an S-shaped value function is formulated to assess the payoffs, and a first-best weighting function considering loss aversion is established within the framework of probability perception. A bilevel optimization approach is employed to estimate the model parameters. The upper level entails a nonlinear programming problem aimed at minimizing the squared difference between observed and predicted strategies, while the lower-level programming seeks the Nash equilibrium solution. Vehicle trajectory data is utilized for model calibration and validation purposes. Validation on the US-101 and I-80 datasets shows that the proposed model achieves detection rates of 92.14% and 92.34%, respectively. The corresponding validation errors are also reported using MAE and RMSE, rather than treating MAE as classification accuracy. Comparative results against representative game-theoretic mandatory lane-changing models further indicate that incorporating prospect-theory-based loss aversion improves both behavioural interpretability and predictive performance.