Reward-driven mixed and stochastic equilibria for efficient and resilient traffic assignment

Regulators adopt incentive strategies to guide urban travel behavior, but travelers deviate from system-optimal routes due to heterogeneous information access and perceptual biases. Traffic assignment quantifies such regulatory impacts on network flow, yet fixed user equilibrium-based research overlooks dynamic incentive penetration and random perceptual responses to incentives. This study explores incentive mechanisms’ effects on route choice and traffic assignment, developing two extended equilibrium models: a Mixed User Equilibrium (MUE) model integrating reward penetration and dynamically adjusted incentives, and a Stochastic User Equilibrium (SUE) model with an adaptive perception coefficient for characterizing random perceptual biases and learning effects. Tailored Frank-Wolfe algorithms are designed to solve both models. Numerical experiments on Braess and Sioux Falls networks verify that rational incentive levels and penetration optimize flow distribution and reduce total network impedance, and the SUE model outperforms the MUE model in reflecting actual travel behavior under high-demand network scenarios.