2016/11/24 by David Evangelista, Evangelista, David, Diogo A. Gomes +1
Decision Sciences · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1611.08232
openalex publication_date 2016/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Mean-field games (MFGs) are models of large populations of rational agents\nwho seek to optimize an objective function that takes into account their\nlocation and the distribution of the remaining agents. Here, we consider\nstationary MFGs with congestion and prove the existence of stationary\nsolutions. Because moving in congested areas is difficult, agents prefer to\nmove in non-congested areas. As a consequence, the model becomes singular near\nthe zero density. The existence of stationary solutions was previously obtained\nfor MFGs with quadratic Hamiltonians thanks to a very particular identity.\nHere, we develop robust estimates that give the existence of a solution for\ngeneral subquadratic Hamiltonians.\n