First-order mean-field games on networks and Wardrop equilibrium

We explore the relationship between Wardrop equilibrium and stationary mean-field games (MFG) on networks with flow-dependent costs. First, we present the notion of Wardrop equilibrium and the first-order MFG model on networks. We then reformulate the MFG problem into a road traffic problem, establishing that the flow distribution of the MFG solution is the corresponding Wardrop equilibrium. Next, we prove that the solution of the MFG model can be recovered using the corresponding Wardrop equilibrium. Next, we examine the cost properties and calibrate MFG with respect to travel cost problems on networks. We propose a novel calibration approach for MFGs. Additionally, we demonstrate that non-monotonic MFGs can be generated by even simple travel costs.