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

Author

Engwerda, J.

Author_Institution

Dept. of Econ. & Oper., Tilburg Univ., Tilburg, Netherlands

Volume

60

Issue

11

fYear

2015

Firstpage

3101

Lastpage

3106

Abstract

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 ∈ ℝ²^N ×²^N. Since the size of U increases exponentially on N, the algorithm only applies for games where the number of players is not too large.

Keywords

Riccati equations; differential games; eigenvalues and eigenfunctions; feedback; linear systems; matrix algebra; algebraic Riccati equation; eigenvalue-eigenvector problem; linear feedback Nash equilibrium; numerical algorithm; parametrized matrix; scalar affine quadratic differential game; Eigenvalues and eigenfunctions; Games; Mathematical model; Polynomials; Riccati equations; Vectors; Computational methods; Riccati equations; computational methods; game theory; linear systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2015.2411914

Filename

7058424