  Mean-field games (MFGs) are models of large populations of rational agents
who seek to optimize an objective function that takes into account their
location and the distribution of the remaining agents. Here, we consider
stationary MFGs with congestion and prove the existence of stationary
solutions. Because moving in congested areas is difficult, agents prefer to
move in non-congested areas. As a consequence, the model becomes singular near
the zero density. The existence of stationary solutions was previously obtained
for MFGs with quadratic Hamiltonians thanks to a very particular identity.
Here, we develop robust estimates that give the existence of a solution for
general subquadratic Hamiltonians.
