A Kind of Stochastic Linear-Quadratic Stackelberg Differential Game with Overlapping Information
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- 英文论文题名：A Kind of Stochastic Linear-Quadratic Stackelberg Differential Game with Overlapping Information
- 论文作者：Jingtao Shi ; Guangchen Wang ; Jie Xiong
- 英文论文作者：Jingtao Shi ; Guangchen Wang ; Jie Xiong ; School of Mathematics ; Shandong University ; School of Control Sciences and Engineering ; Shandong University ; Department of Mathematics ; Faculty of Science and Technology ; University of Macau
- 年：2017
- 作者机构：School of Mathematics,Shandong University;School of Control Sciences and Engineering,Shandong University;Department of Mathematics,Faculty of Science and Technology,University of Macau;
- 英文论文关键词：Stackelberg differential game ; stochastic linear-quadratic optimal control ; overlapping information ; maximum principle ; stochastic filtering
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O225
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：269k
- 原文格式：D
- 会议级别：全国
摘要
This paper is concerned with a kind of stochastic linear-quadratic Stackelberg differential game with overlapping information. Here the term "overlapping" means that the follower's and the leader's information have some joint part, while they have no inclusion relation. Optimal controls of the follower and the leader's are proved by the stochastic maximum principle, the direct calculation of the derivative of the cost functional and stochastic filtering. A new system of Riccati equations is introduced to represent the state feedback of the Stackelberg equilibrium strategy.
This paper is concerned with a kind of stochastic linear-quadratic Stackelberg differential game with overlapping information. Here the term "overlapping" means that the follower's and the leader's information have some joint part, while they have no inclusion relation. Optimal controls of the follower and the leader's are proved by the stochastic maximum principle, the direct calculation of the derivative of the cost functional and stochastic filtering. A new system of Riccati equations is introduced to represent the state feedback of the Stackelberg equilibrium strategy.
This paper is concerned with a kind of stochastic linear-quadratic Stackelberg differential game with overlapping information. Here the term "overlapping" means that the follower's and the leader's information have some joint part, while they have no inclusion relation. Optimal controls of the follower and the leader's are proved by the stochastic maximum principle, the direct calculation of the derivative of the cost functional and stochastic filtering. A new system of Riccati equations is introduced to represent the state feedback of the Stackelberg equilibrium strategy.
引文
[1]A.Bagchi,T.Basar,Stackelberg strategies in linear-quadratic stochastic differential games,J.Optim.Theory Appl.,35(3):443–464,1981.
[2]A.Bensoussan,S.Chen,and S.Sethi,The maximum principle for global solutions of stochastic Stackelberg differential games.SIAM J.Control Optim.,53(4):1956–1981,2015.
[3]D.Chang,H.Xiao,Linear quadratic nonzero sum differential games with asymmetric information,Math.Prob.Engin.,Vol.2014,Article ID 262314,11 pages.
[4]B.?ksendal,L.Sandal,and J.Ub?e,Stochastic Stackelberg equilibria with applications to time dependent newsvendor models,J.Econ.Dyna.&Control,37(7):1284–1299,2013.
[5]J.Shi,G.Wang,A new kind of linear-quadratic leader-follower stochastic differential game,in Proc.10th IFAC Symposium on Nonlinear Control Systems,August 23-25,322–326,Monterey,USA,2016.
[6]J.Shi,G.Wang,and J.Xiong,Leader-follower stochastic differential games with asymmetric information and applications,Automatica,63:60–73,2016.
[7]J.Shi,G.Wang,and J.Xiong,Linear-quadratic stochastic Stackelberg differential game with asymmetric information,Sci.China Inf.Sci.,60(1),2017.doi:10.1007/s11432-016-0654-y
[8]M.Simaan,J.Cruz Jr,On the Stackelberg game strategy in non-zero games,J.Optim.Theory Appl.,11(5):533–555,1973.
[9]H.von Stackelberg,The Theory of the Market Economy.London:Oxford University Press,1952.
[10]J.Xiong,An Introduction to Stochastic Filtering Theory,London:Oxford University Press,2008.
[11]J.Xu,H.Zhang,Sufficient and necessary open-loop Stackelberg strategy for two-player game with time delay,IEEE Trans.Cyber.,46(2):438–449,2016.
[12]J.Xu,H.Zhang,T.Chai,Necessary and sufficient condition for two-player Stackelberg strategy,IEEE Trans.Autom.Control,60(5):1356–1361,2015.
[13]J.Yong.A leader-follower stochastic linear quadratic differential game,SIAM J.Control Optim.,41(4):1015–1041,2002.
[2]A.Bensoussan,S.Chen,and S.Sethi,The maximum principle for global solutions of stochastic Stackelberg differential games.SIAM J.Control Optim.,53(4):1956–1981,2015.
[3]D.Chang,H.Xiao,Linear quadratic nonzero sum differential games with asymmetric information,Math.Prob.Engin.,Vol.2014,Article ID 262314,11 pages.
[4]B.?ksendal,L.Sandal,and J.Ub?e,Stochastic Stackelberg equilibria with applications to time dependent newsvendor models,J.Econ.Dyna.&Control,37(7):1284–1299,2013.
[5]J.Shi,G.Wang,A new kind of linear-quadratic leader-follower stochastic differential game,in Proc.10th IFAC Symposium on Nonlinear Control Systems,August 23-25,322–326,Monterey,USA,2016.
[6]J.Shi,G.Wang,and J.Xiong,Leader-follower stochastic differential games with asymmetric information and applications,Automatica,63:60–73,2016.
[7]J.Shi,G.Wang,and J.Xiong,Linear-quadratic stochastic Stackelberg differential game with asymmetric information,Sci.China Inf.Sci.,60(1),2017.doi:10.1007/s11432-016-0654-y
[8]M.Simaan,J.Cruz Jr,On the Stackelberg game strategy in non-zero games,J.Optim.Theory Appl.,11(5):533–555,1973.
[9]H.von Stackelberg,The Theory of the Market Economy.London:Oxford University Press,1952.
[10]J.Xiong,An Introduction to Stochastic Filtering Theory,London:Oxford University Press,2008.
[11]J.Xu,H.Zhang,Sufficient and necessary open-loop Stackelberg strategy for two-player game with time delay,IEEE Trans.Cyber.,46(2):438–449,2016.
[12]J.Xu,H.Zhang,T.Chai,Necessary and sufficient condition for two-player Stackelberg strategy,IEEE Trans.Autom.Control,60(5):1356–1361,2015.
[13]J.Yong.A leader-follower stochastic linear quadratic differential game,SIAM J.Control Optim.,41(4):1015–1041,2002.