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

WANG Guangchen · ZHANG Susu

Journal of Systems Science & Complexity ›› 2020, Vol. 33 ›› Issue (5) : 1383-1401.

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PDF(255 KB)
Journal of Systems Science & Complexity ›› 2020, Vol. 33 ›› Issue (5) : 1383-1401. DOI: 10.1007/s11424-020-9025-z

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

  • WANG Guangchen · ZHANG Susu
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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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WANG Guangchen · ZHANG Susu. A Mean-Field Linear-Quadratic Stochastic Stackelberg Differential Game with one Leader and Two Followers. Journal of Systems Science and Complexity, 2020, 33(5): 1383-1401 https://doi.org/10.1007/s11424-020-9025-z
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