This thesis studies nonlinear stationary mean field games and provides a way to find an approximate solution of a particular class of problems. In the general case, it is very difficult to find a solution of a mean field game because it requires to solve of a system of partial differential equations. The goal of the work presented in this thesis is to show a procedure to find an approximate local equilibrium for a class of nonlinear mean field games with the cost function of a particular form. The proposed technique is characterized by the fact that it permits to solve two algebraic inequalities instead of a system of PDEs. It is local and formally proved in a neighborhood of the origin. Moreover, we only focus on stationary solutions i.e. functions that describe players behavior due the application of an optimal control after a long time. Finally, a numerical example is introduced and the effectiveness of the proposed technique is shown.
