Abstract
In this paper, we consider the continuous-time linear-quadratic Stackelberg game for descriptor systems with three levels of hierarchy in the decision-making process. Sufficient conditions for the existence of the linear feedback closed-loop Stackelberg (LFCLS) strategies for both player P1 at the top of the hierarchy and player P2 at the second level of the hierarchy are derived. The obtained LFCLS strategy for P1 forces the other players to act so as to jointly minimize the cost function of P1. The obtained LFCLS strategy for P2 forces player P3 to jointly minimize the cost function of P2 under the declared LFCLS strategy of P1. An illustrative example is included to show the exact existence of such LFCLS strategies.
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Communicated by G. Leitmann
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Xu, H., Mizukami, K. Linear feedback closed-loop Stackelberg strategies for descriptor systems with multilevel hierarchy. J Optim Theory Appl 88, 209–231 (1996). https://doi.org/10.1007/BF02192030
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DOI: https://doi.org/10.1007/BF02192030