DISCRETE-TIME RICCATI EQUATIONS IN OPEN-LOOP STACKELBERG GAMES WITH TIME PREFERENCE RATES

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.