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A Mean-Field Linear-Quadratic Stochastic Stackelberg Differential Game with one Leader and Two Followers

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Abstract

This paper is concerned with a linear-quadratic (LQ) stochastic Stackelberg differential game with one leader and two followers, where the game system is governed by a mean-field stochastic differential equation (MF-SDE). By maximum principle and verification theorem, the open-loop Stackelberg solution is expressed as a feedback form of the state and its mean with the help of three systems of Riccati equations.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Guangchen Wang

  2. No. 12 Middle School Jinan Shandong, Jinan, 250022, China

    Susu Zhang

Authors
  1. Guangchen Wang
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  2. Susu Zhang
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Corresponding author

Correspondence to Susu Zhang.

Additional information

This paper was supported in part by the Fund for Innovative Research Groups of NSFC under Grant No. 61821004, the Key Program of NSFC under Grant Nos. 61633015 and 11831010, and the NSFC for Distinguished Young Scholars under Grant No. 61925306.

This paper was recommended for publication by Editor-in-Chief CHEN Jie.

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Wang, G., Zhang, S. A Mean-Field Linear-Quadratic Stochastic Stackelberg Differential Game with one Leader and Two Followers. J Syst Sci Complex 33, 1383–1401 (2020). https://doi.org/10.1007/s11424-020-9025-z

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  • DOI: https://doi.org/10.1007/s11424-020-9025-z

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