Continuous price and flow dynamics of tradable mobility credits

• Evolution dynamics of price and perceived travel times under a tradable credit scheme is examined.
• Travelers’ learning behavior of path choice is characterized by a continuous-time dynamic model.
• Price evolution is governed by the excess credit demand in the credit trading market.
• Existence and uniqueness of the equilibria are established under mild conditions.

This study examines the price and flow dynamics under a tradable credit scheme, when the credits can be traded in a free market. A continuous dynamic model in a finite time horizon is proposed to describe the travelers’ learning behavior and the evolution of network flows and credit price, and then the existence and uniqueness of the equilibria are established. The conditions for stability and convergence of the dynamic system as the time horizon extends to infinity and the impact of limited implementation time horizon on the system behavior are investigated.