Finite horizon linear quadratic dynamic games for discrete-time stochastic systems with N-players

被引：5

作者：

Zhu, Huai-Nian ^{[1
]}

Zhang, Cheng-Ke ^{[1
]}

机构：

[1] Guangdong Univ Technol, Sch Econ & Commence, Guangzhou 510520, Guangdong, Peoples R China

来源：

OPERATIONS RESEARCH LETTERS | 2016年 / 44卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Pareto optimal strategy; Nash strategy; Discrete-time-stochastic systems; Matrix-valued equations; STATE; STRATEGY;

D O I：

10.1016/j.orl.2016.02.010

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, dynamic games for a class of finite horizon linear stochastic system governed by Ito's difference equation are investigated. Particularly, both Pareto and Nash strategies are discussed. After defining the equilibrium condition, sufficient conditions for the existence of the strategy sets are obtained, which are associated with the solvability of the corresponding generalized difference Riccati equations (GDREs). Furthermore, an iterative algorithm is proposed to solve the related GDREs and a simple numerical example is given to show the reliability and usefulness of the considerable results. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：307 / 312

页数：6

共 16 条

[1]

[Anonymous], 1998, Stochastic differential equations

[2]

[Anonymous], 2000, DIFFERENTIAL GAMES E

[3]

Basar T., 1999, Dynamic Noncooperative Game Theory, Vsecond

[4] Stochastic games for N players [J].

Bensoussan, A ;

Frehse, J .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2000, 105 (03) :543-565

[5] Nash equilibrium payoffs for nonzero-sum stochastic differential games [J].

Buckdahn, R ;

Cardaliaguet, P ;

Rainer, C .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2004, 43 (02) :624-642

[6]

Engwerda J, 2005, LQ dynamic optimization and differential games

[7] INFINITE HORIZON LINEAR QUADRATIC OPTIMAL CONTROL FOR DISCRETE-TIME STOCHASTIC SYSTEMS [J].

Huang, Yulin ;

Zhang, Weihai ;

Zhang, Huanshui .

ASIAN JOURNAL OF CONTROL, 2008, 10 (05) :608-615

[8]

Mukaidani H., 2010, 2010 IEEE International Symposium on Computer-Aided Control System Design (CACSD) part of the IEEE Multi-Conference on Systems & Control (MSC 2010), P761, DOI 10.1109/CACSD.2010.5612859

[9] A numerical analysis of the Nash strategy for weakly coupled large-scale systems [J].

Mukaidani, Hiroaki .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2006, 51 (08) :1371-1377

[10] Stackelberg strategies for stochastic systems with multiple followers [J].

Mukaidani, Hiroaki ;

Xu, Hua .

AUTOMATICA, 2015, 53 :53-59

← 1 2 →