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

Mean Field Games with monotonous interactions through the law of states and controls of the agents