On the uniqueness of non-reducible multi-player control problems

In this article, we consider a special class of generalized Nash equilibrium problems that cannot be reduced to a single player control problem. We find a sufficient condition, that proves the existence and uniqueness of solutions. Problems of this type can be solved by a semi-smooth Newton method. Applying the same condition as needed for the uniqueness of solutions, 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. Numerical examples are presented to support the theoretical findings.

Automated summary

This article examines a special class of generalized Nash equilibrium problems that cannot be reduced to a single player control problem, finding a sufficient condition for the existence and uniqueness of solutions and presenting a solving method. Numerical examples are used to support the theoretical findings.