On Non-Reducible Multi-Player Control Problems and their Numerical Computation

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.