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Feedback Stackelberg Solution for Mean-Field Type Stochastic Systems with Multiple Followers

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Abstract

This paper discusses feedback Stackelberg strategies for the continuous-time mean-field type stochastic systems with multiple followers in infinite horizon. First, optimal control problems of the followers are studied in the sense of Nash equilibrium. With the help of a set of generalized algebraic Riccati equations (GAREs), sufficient conditions for the solvability are put forward. Then, the leader faces a constrained optimal control problem by transforming the cost functional into a trace criterion. Employing the Karush-Kuhn-Tucker (KKT) conditions, necessary conditions are presented in term of the solvability of the cross-coupled stochastic algebraic equations (CSAEs). Moreover, feedback Stackelberg strategies are obtained based on the solutions of the CSAEs. In addition, an iterative scheme is introduced to obtain efficiently the solutions of the CSAEs. Finally, an example is given to shed light on the effectiveness of the proposed results.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255000, China

    Yaning Lin

  2. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, China

    Weihai Zhang

Authors
  1. Yaning Lin
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  2. Weihai Zhang
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Corresponding author

Correspondence to Yaning Lin.

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The authors declare no conflict of interest.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 61903234 and 61973198.

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Cite this article

Lin, Y., Zhang, W. Feedback Stackelberg Solution for Mean-Field Type Stochastic Systems with Multiple Followers. J Syst Sci Complex 36, 1519–1539 (2023). https://doi.org/10.1007/s11424-023-1145-9

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  • DOI: https://doi.org/10.1007/s11424-023-1145-9

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