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.
- Riccati equations
- differential games
- eigenvalues and eigenfunctions
- linear systems
- matrix algebra