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A new feedback form of open-loop Stackelberg strategy in a general linear-quadratic differential game

  • *Corresponding author: Yu Li

    *Corresponding author: Yu Li 
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  • In this paper, we consider a general form of linear-quadratic Stackelberg deterministic differential game model, which consists of one leader and one follower. Each of their utility functions includes all possible squared terms, cross terms and single terms of states and controls of the two players, and constant terms. The time-consistent state feedback form of Stackelberg equilibrium strategy is obtained. Its explicit expression is in terms of the solutions of three decoupled symmetric Riccati differential equations. These decoupled symmetric Riccati differential equations are independent of the state and can be solved backward in time one by one. The proposed model and theory are applied to some classical Stackelberg games.

    Mathematics Subject Classification: Primary: 91A65, 49N10; Secondary: 90B06.


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  • Figure 1.  $ c_e = 0.5, 1.0, 1.5, 2.0 $ from left to right and from up to down

    Figure 2.  The optimal polices under promotion

    Figure 3.  Zoom in at $ t_s $ and $ t_f $

    Figure 4.  The optimal polices under promotion

    Figure 5.  Zoom in at $ t_s $ and $ t_f $

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