2022/07/04 by Fatimah Al Saleh, Tigran Bakaryan, Saleh, Fatimah Al +6 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · Social Sciences · #49N80 #65M99 #91A13 #91A16 #Analysis of PDEs (math.AP) #Economic theories and models #FOS: Mathematics #Numerical Analysis (math.NA) #Transportation Planning and Optimization #cs.NA #math.AP #math.NA #msc:49N80 #msc:65M99 #msc:91A13 #msc:91A16
paper · pdf · doi:10.48550/arxiv.2207.01397
44 pages, 11 figures
arxiv created 2022/07/04 · openalex publication_date 2022/07/04 · arxiv updated 2022/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Here, we examine the Wardrop equilibrium model on networks with flow-dependent costs and its connection with stationary mean-field games (MFG). In the first part of this paper, we present the Wardrop and the first-order MFG models on networks. Then, we show how to reformulate the MFG problem into a Wardrop problem and prove that the MFG solution is the Wardrop equilibrium for the corresponding Wardrop problem. Moreover, we prove that the solution of the MFG problem can be recovered using the solution to the associated Wardrop problem. Finally, we study the cost properties and the calibration of MFG with Wardrop travel cost problems. We describe a novel approach to the calibration of MFGs. Further, we show that even simple travel costs can give rise to non-monotone MFGs.