  In this article we consider a special class of Nash equilibrium problems that
cannot be reduced to a single player control problem. Problems of this type can
be solved by a semi-smooth Newton method. Applying results from the established
convergence analysis we derive superlinear convergence for the associated
Newton method and the equivalent active-set method. We also provide detailed
finite element discretizations for both methods. Several numerical examples are
presented to support the theoretical findings.
