Weakly coupled mean-field game systems
  Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized problem. Finally, by a limiting procedure, we obtain solutions to the MFG problem. 
Diogo A. Gomes, Stefania Patrizi
math.AP