广东工业大学学报 ›› 2012, Vol. 29 ›› Issue (3): 35-38.doi: 10.3969/j.issn.1007-7162.2012.03.006

• 综合研究 • 上一篇    下一篇

一类不定仿线性二次型随机微分博弈的鞍点均衡策略

朱怀念1，张成科2，李云龙1，杨超进1   

  1. 广东工业大学 1.管理学院； 2.经济与贸易学院，广东 广州 510520
  • 收稿日期:2012-02-21 出版日期:2012-09-20 发布日期:2012-09-20
  • 作者简介:朱怀念(1985-)，男，博士研究生. 主要研究方向为管理系统工程、博弈论.
  • 基金资助:

    国家自然科学基金资助项目(71171061);广东省自然科学基金资助项目(S2011010004970)

Saddlepoint Equilibrium Strategy for a Class of Indefinite Affinequadratic Stochastic Differential Games

Zhu Huainian1, Zhang Chengke2, Li Yunlong1, Yang Chaojin1   

  1. 1. School of Management; 2. School of Economics & Commence, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2012-02-21 Online:2012-09-20 Published:2012-09-20

HTML

PDF (PC)

3198

摘要： 研究了一类连续时间不定仿线性二次型随机微分博弈的鞍点均衡问题，在It微分的意义下，通过引入一个广义Riccati微分方程(GRDE)，证明了该GRDE的可解性是相应随机微分博弈问题均衡策略存在的一个充分必要条件，同时给出了最优策略闭环形式的显式解以及最优性能指标值，所得的结论拓展了已有的有关确定性微分博弈和权系数矩阵正定情形下的随机微分博弈的结果.

关键词: 随机微分博弈；鞍点均衡；广义Riccati微分方程

Abstract: It discusses the saddlepoint equilibrium strategy for indefinite affinequadratic stochastic differential games in continuous time. By introducing a generalized Riccati differential equation (GRDE), it proves that under the condition of Its differential rule, the solvability of GRDE is both the sufficient and necessary condition for the existence of equilibrium strategies. Meanwhile, the explicit solution of equilibrium strategies with closed forms and the optimal value of cost function are obtained. The results expand the previous results of the ordinary deterministic differential games and stochastic differential games with definite weight cost matrices.

Key words: stochastic differential games; saddlepoint equilibrium; generalized Riccati differential equation

［1］ Rufus Isaacs. Differential Games ［M］. New York:John Wiley and Sons, 1965.

［2］ Friedman, A. Differential Games ［M］. New York:WileyInterscience, 1971.

［3］ Tamer Basar, Geert Jan Olsder. Dynamic Noncooperative Game Theory ［M］.  New York:Academic Press, 1991.

［4］ Engelbert J Dockner, Steffen Jorgensen, Ngo Van Long, et al. Differential Games in Economics and Management Science ［M］. Cambridge, UK: Cambridge University Press, 2000.

［5］ David W K Yeung, Leon A Petrosjan. Cooperative Stochastic Differential Games ［M］.USA:Springer, 2005.

［6］ Kandethody M, Ramachandran, Chris P Tsokos. Stochastic Differential Games. Theory and Applications ［M］. USA: Springer, 2012.

［7］ Zhou, X Y, Li D. Continuoustime meanvariance portfolio selection: a stochastic LQ framework ［J］. Appl  Math Optim, 2000, 42(1):1933.

［8］ Chen S, Li X, Zhou X Y. Stochastic linear quadratic regulators with indefinite control weight costs ［J］. SIAM J Control Optim,1998,36(5):16851702.

［9］ Chen S, Zhou  X Y. Stochastic linear quadratic regulators with indefinite control weight costs. II ［J］. SIAM J Control Optim,2000,39(4):10651081.

［10］ Mustapha Ait Rami, Zhou Xunyu. Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls ［J］. IEEE Transactions on Automatic Control, 2000,45(6):11311143.
［9］ Guo S,Wu X. Deriving private information from arbitrarily projected data［J］. Advances in Knowledge Discovery and Data Mining, 2007: 8495.

［10］ Kargupta H, Datta S, Wang Q, et al. On the privacy preserving properties of random data perturbation techniques［C］. Proceedings of the 3rd IEEE International Conference on Data Mining, Melbourne, FL, USA, November 2003.

［11］ Guo S. Analysis of and techniques for privacy preserving data mining［M］. Ann Arbor: ProQuest Information and Learning Company, 2007.

［12］ Liu Kun. Multiplicative data perturbation for privacy preserving data mining［D］. Baltimore, MD, USA: University of Maryland Baltimore County, 2007.

［13］Huang Z, Du W,Chen B. Deriving private information from randomized data［C］. Proceedings of the 2005 ACM 〖JP2〗SIGMOD Conference, Baltimroe, MD, June 2005: 3748.

［14］ Aggarwal C C, Yu P S. A condensation based approach to privacy preserving data mining［C］. Proceedings of the 9th International Conference on Extending Database Technology (EDBT’04), Heraklion, Crete, Greece, March 2004: 183-199.

［15］ 肖岳.移动数据的智能分析与隐私保护［D］.广州：广东工业大学，2011.

Xiao Yue. Intelligent analysis and privacyprotection of mobile data［D］. Guangzhou: Guangdong University of Technology, 2011.

［16］ 聂跃光.基于密度聚类的空间数据挖掘算法研究［D］.太原：太原科技大学，2008.

Nie Yueguang. Study of spatial data mining algorithm based on density clustering［D］. Taiyuan: Taiyuan University of Science and Technology, 2008.
No related articles found!
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2017 《广东工业大学学报》编辑部
地址：广州市东风东路729号广东工业大学 邮编：510090
电话：020-37626653,020-37626139,020-37626396
邮箱：xbzrb@gdut.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发