Discrete time riccati equations in open loop nash games for descriptor systems

In this paper we study difference equations appearing in the necessary optimality conditions of noncooperative open loop Nash games with the players are given control to descriptor systems. Since these equations are coupled nonsymmetric Riccati difference equations, their qualitative behaviour is essentially different from that of standard (symmetric) Riccati equations. Moreover we study also the properties of the solutions of the corresponding algebraic Riccati equations.