We propose a new method for solving nonlinear dynamic tracking games using a meta-heuristic approach. In contrast to ‘traditional’ methods based on linear-quadratic (LQ) techniques, this derivative-free method is very flexible with regard to the objective function specification. The proposed method is applied to a three-player dynamic game and tested versus a derivative-dependent method in approximating solutions of different game specifications. In particular, we consider a dynamic game between fiscal (played by national governments) and monetary policy (played by a central bank) in a monetary union. Apart from replicating results of the LQ-based techniques in a standard setting, we solve two ‘non-standard’ extensions of this game (dealing with an inequality constraint in a control variable and introducing asymmetry in penalties of the objective function), identifying both a cooperative Pareto and a non-cooperative open-loop Nash equilibria, where the traditional methods are not applicable. We, thus, demonstrate that the proposed method allows one to study more realistic problems and gain better insights for economic policy.