The Suboptimal Nash Equilibrium Strategy For Two-person Continuous Nonlinear-quadratic Differential Game

被引：0

作者：

Zhang Chengke ^{[1
]}

Bin Ning ^{[1
]}

Sun Peihong ^{[1
]}

机构：

[1] Guangdong Univ Technol, Sch Econ & Management, Guangzhou 510090, Guangdong, Peoples R China

来源：

ICPOM2008: PROCEEDINGS OF 2008 INTERNATIONAL CONFERENCE OF PRODUCTION AND OPERATION MANAGEMENT, VOLUMES 1-3 | 2008年

关键词：

nonlinear systems; differential game; Nash equilibrium; successive approximation approach;

D O I：

暂无

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：

This paper deals with a class of Nash equilibrium strategy problems for two-person continuous nonlinear-quadratic dynamic game. A successive approximation approach (SAA) is presented. By using SAA, the nonlinear system Nash equilibrium problem is transformed into a sequence of special non-homogeneous linear two-point boundary value (TPBV). The finite-step iteration manner of the Nash equilibrium strategy is derived, and the uniformity and absolutization of the algorithm's convergence has been proved.

引用

页码：1739 / 1742

页数：4

共 17 条

[11] An Alternating Direction Method for Nash Equilibrium of Two-Person Games with Alternating Offers
Peng, Zheng
Zhu, Wenxing
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2013, 157 (02) : 533 - 551
[12] An Alternating Direction Method for Nash Equilibrium of Two-Person Games with Alternating Offers
Zheng Peng
Wenxing Zhu
Journal of Optimization Theory and Applications, 2013, 157 : 533 - 551
[13] Computing lexicographically safe Nash equilibria in finite two-person games with tight game forms given by oracles
Gurvich, Vladimir
Naumova, Mariya
DISCRETE APPLIED MATHEMATICS, 2023, 340 : 53 - 68
[14] Linear-quadratic stochastic two-person nonzero-sum differential games: Open-loop and closed-loop Nash equilibria
Sun, Jingrui
Yong, Jiongmin
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2019, 129 (02) : 381 - 418
[15] Continuous and impulse controls differential game in finite horizon with Nash-equilibrium and application
El Asri, Brahim
Ibn, Hafid Lalioui
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2023, 424
[16] An adaptive differential evolution algorithm based on relaxation strategy to realize the Nash equilibrium of multi-oligopoly game
Li, Huimin
Xiang, Shuwen
Huang, Shiguo
Luo, Enquan
QUAESTIONES MATHEMATICAE, 2024, 47 (08) : 1571 - 1587
[17] APPLICATION OF LYAPUNOV-POINCARE<acute accent> METHOD OF SMALL PARAMETER FOR NASH AND BERGE EQUILIBRIUM DESIGNING IN ONE DIFFERENTIAL TWO-PLAYER GAME
Zhukovskiy, V. I.
Zhukovskaya, L., V
Sachkov, S. N.
Sachkova, E. N.
VESTNIK UDMURTSKOGO UNIVERSITETA-MATEMATIKA MEKHANIKA KOMPYUTERNYE NAUKI, 2023, 33 (04): : 601 - 624

← 1 2 →