Slow and steady wins the race: Approximating Nash equilibria in nonlinear quadratic tracking games

Abstract

We propose a meta-heuristic approach for solving nonlinear dynamic tracking games. In contrast to more "traditional" methods based on linear-quadratic (LQ) techniques, this derivative-free method is very flexible (e.g. to introduce inequality constraints). The meta-heuristic is applied to a three-player dynamic game and tested versus derivative-dependent method in approximating Nash solution in different game specifications. We demonstrate the superiority of the proposed approach in identifying Nash equilibria, where LQ methods are not applicable