A numerical algorithm to find soft-constrained Nash equilibria in scalar LQ-games

摘要

This paper provides a numerical algorithm to calculate all soft-constrained Nash equilibria in a regular scalar indefinite linear-quadratic game. The algorithm is based on the calculation of the eigenstructure of a certain matrix. The analysis follows the lines of the approach taken by Engwerda (2003) to calculate the solutions of a set of scalar coupled feedback Nash algebraic Riccati equations.