Day-to-day Traffic Dynamics with Strategic Commuters

In the era of connected and automated mobility, commuters (connected drivers or automated vehicles) will possess strong computation capability and their travel decisions can be algorithmic and strategic. This paper investigates the day-to-day travel choice evolution of such strategic commuters who are capable of long-term planning and computation. We model the commute problem as a mean field game and examine the mean field equilibrium to derive the evolution of the network traffic flow pattern. The proposed model is general and can be tailored to various travel choices such as route or departure time. Under various conditions, we prove the existence and uniqueness of the day-to-day equilibrium traffic evolution pattern as well as its convergence to stationarity. Connection with traditional Wardropian equilibrium is established by examining the physical interpretation of the stationary solution