Linear-quadratic stochastic Stackelberg differential game with asymmetric information

Abstract

This paper is concerned with a linear-quadratic stochastic Stackelberg differential game, where players have asymmetric roles, with one leader and one follower in the context of two-person game. It is required that the information available to the follower is a sub-σ-algebra of the one of the leader. By maximum principle and optimal filtering, a feedback Stackelberg equilibrium of the game is given. A special example is used to elaborate the result.

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Acknowledgements

SHI acknowledges the financial support from National Natural Science Fundation of China (Grant No. 11571205) and Natural Science Fund for Distinguished Young Scholars of Shandong Province of China (Grant No. JQ201401). WANG acknowledges the financial support from National Natural Science Fundation for Excellent Young Scholars of China (Grant No. 61422305), National Natural Science Fundation of China (Grant No. 11371228), Natural Science Fund for Distinguished Young Scholars of Shandong Province of China (Grant No. JQ201418), and Research Fund for the Taishan Scholar Project of Shandong Province of China. XIONG acknowledges the financial support from Macau Science and Technology Development Fund (Grant No. FDCT 025/2016/A1) and Multi-Year Research Grant of the University of Macau (Grant No. MYRG2014-00015-FST). The material in Section 3 of this work was partly presented at the 35th Chinese Control Conference, Chengdu, July 27–29, 2016. The authors thank three anonymous referees for their careful reading and valuable comments which have led to significant improvement on the previous version of the paper.

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Correspondence to Guangchen Wang.

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The authors declare that they have no conflict of interest.

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Shi, J., Wang, G. & Xiong, J. Linear-quadratic stochastic Stackelberg differential game with asymmetric information. Sci. China Inf. Sci. 60, 092202 (2017). https://doi.org/10.1007/s11432-016-0654-y

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Keywords

  • stochastic Stackelberg differential game
  • linear-quadratic control
  • asymmetric information
  • conditional mean-field forward-backward stochastic differential equation
  • optimal filtering