Hello everyone,
Can someone help me with references to solve a closed loop Stackelberg game for linear differential dynamic games for continuous system. The game is infinite horizon. Thank you.
I guess that you are asking for an exact solution for such a differential game. This is a very difficult task, and you cannot expect in general to determine an analytic solution. In my opinion, the only chance to find such a solution is by the Lie group analysis. Since you study a Stackelberg differential game in closed loop strategies, you will get a coupled system of partial differential equations. If this coupled system of PDEs is linear homogeneous, then one can even expect an exact solution without the Lie group method. However, if it is nonlinear and the parameter space of your model is quite large, then everything depends if you are able to find the Lie symmetries. From those and the invariant surface condition you might be able to derive an analytic solution of the optimal value functions or at least to solve them by quadrature.
To get an idea how to proceed by such an analysis, I recommend to download my most recent discussion paper that solves the arising PDEs of a dynamic resource problem by the Lie group method. The manuscript can be found at the URL
https://gigamove.rz.rwth-aachen.de/d/id/PtByGNhPJJobCj
till 30.11.2017. In case that you miss the date, then contact me, and I will open a new link. Finally, note that this is a very preliminary version, and not everything should be taken as face value.
I hope this answer gives you some idea and help to solve your Stackelberg differential game. Good luck.
Update: 28.01.2018
The mentioned paper is now online at
Working Paper Applying Lie Group Analysis to a Dynamic Resource Management Problem
Comments and suggestion of improvements are highly appreciated.
You should read the book of Basar and Olsder
Article Dynamic Non-Cooperative Game Theory
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