Discrete-Time Riccati Equations in Open-Loop Stackelberg Games with Time Preference Rates

Marc Jungers (1)

1 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie

In this paper the Discrete-Time Riccati Equations in Open-loop Linear-Quadratic Stackelberg Games are studied. In the extended case of games including time preference rates into criteria of the players, it is pointed out that a matrix pencil is characteristic of these Discrete-Time Riccati Equations. A property of the distribution of the characteristic matrix pencil eigenvalues is studied. An approach using deflating subspace of matrix pencil helps to solve the discrete-time Riccati equations. An example illustrates the main result.

Mots clés: matrix pencil.; Linear-quadratic discrete time games; Stackelberg strategy; symplectic matrix; time preference rate; Discrete time Algebraic Riccati equations; matrix pencil

Domaines: Automatique

Marc Jungers. Discrete-Time Riccati Equations in Open-Loop Stackelberg Games with Time Preference Rates. 3rd IFAC Symposium on System, Structure and Control (SSSC), Oct 2007, Foz do Iguaçu, Brazil. pp.CD-ROM. ⟨hal-00201424⟩