Solvability condition for a nonsymmetric Riccati equation appearing in stackelberg games

Open-loop Stackelberg games are conceptual very interesting particularly for applications which contain a hierarchical structure. The existence of unique Stackelberg equilibria was shown to be tied to the existence of solutions to certain nonsymmetric Riccati equations, which are hard to solve. The paper reveals a connection between solutions of a standard algebraic Riccati equation and a nonsymmetric algebraic Riccati equation. As a consequence easy veri£able conditions are obtained to ensure a Stackelberg equilibrium, which makes these type of games accessible to applications.