On the solution set of the scalar feedback Nash algebraic Riccati equations

In this note we analyse Uie sei of scalar algebraic Riccati equations (ARE) that play an important role in finding feedback Nash equilibria of the scalar multi-player linear-quadratic differential game. We show that in general there exists more than one solution of the (ARE) that gives rise to a Nash equilibrium. In particular we analyse the number of equilibria as a function of the state-feedback parameter.