A Numerical Algorithm to Find All Feedback Nash Equilibria in Scalar Affine Quadratic Differential Games

被引：4

作者：

Engwerda, J. ^{[1
]}

机构：

[1] Tilburg Univ, Dept Econometr & Operat, NL-5000 LE Tilburg, Netherlands

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2015年 / 60卷 / 11期

关键词：

Computational methods; game theory; linear systems; Riccati equations; RICCATI-EQUATIONS; OPTIMIZATION; EXISTENCE;

D O I：

10.1109/TAC.2015.2411914

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This note deals with solving scalar coupled algebraic Riccati equations. These equations arise in finding linear feedback Nash equilibria of the scalar N-player affine quadratic differential game. A numerical procedure is provided to compute all the stabilizing solutions. The main idea is to reformulate the Riccati equations into an extended eigenvalue-eigenvector problem for a specific parametrized matrix U is an element of IR2N x (2N). Since the size of U increases exponentially on N, the algorithm only applies for games where the number of players is not too large.

引用

页码：3101 / 3106

页数：6

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