  We consider a class of Mean Field Games in which the agents may interact
through the statistical distribution of their states and controls. It is
supposed that the Hamiltonian behaves like a power of its arguments as they
tend to infinity, with an exponent larger than one. A monotonicity assumption
is also made. Existence and uniqueness are proved using a priori estimates
which stem from the monotonicity assumptions and Leray-Schauder theorem.
Applications of the results are given.
