Title :
A Numerical Algorithm to Find All Feedback Nash Equilibria in Scalar Affine Quadratic Differential Games
Author_Institution :
Dept. of Econ. & Oper., Tilburg Univ., Tilburg, Netherlands
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 ∈ ℝ2N ×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.
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;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2015.2411914
