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A leader-follower stochastic linear quadratic differential game with time delay

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Abstract

In this paper, we are concerned with the leader-follower stochastic differential game of Itô type with time delay appearing in the leader’s control. The open-loop solution is explicitly given in the form of the conditional expectation with respect to several symmetric Riccati equations. The key technique is to establish the nonhomogeneous relationship between the forward variables and the backward ones obtained in the optimization problems of both the follower and the leader.

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Acknowledgements

This work was supported by Taishan Scholar Construction Engineering by Shandong Government, National Natural Science Foundation of China (Grant Nos. 61403235, 61104050, 11201264, 61573221, 61633014), Natural Science Foundation of Shandong Province (Grant Nos. ZR2011AQ012, ZR2014FQ011).

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Correspondence to Huanshui Zhang.

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Cite this article

Xu, J., Shi, J. & Zhang, H. A leader-follower stochastic linear quadratic differential game with time delay. Sci. China Inf. Sci. 61, 112202 (2018). https://doi.org/10.1007/s11432-017-9293-4

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Keywords

  • time delay
  • leader-follower differential game
  • open-loop strategy
  • Riccati equation