Properties of coupled Riccati equations in Stackelberg games with time preference rate
Résumé
In this paper we deal with Stackelberg equilibrium in linear-quadratic games when a time preference rate is introduced in the players' cost functions with an open loop information structure. We apply general necessary conditions from \cite{Simaan1,Simaan2} to our framework with a time preference rate. Such conditions lead to a set of coupled differential (or algebraic) Riccati equations. Necessary conditions for constant real solutions for the algebraic Riccati equations (ARE) are derived. We give a bound for the number of real, constant and stabilizing solutions. When many solutions of (ARE) exist, a robustness study gives informations to choose the most robust control. A numerical example illustrates these results.