A series solution for coupled algebraic Riccati type equations from closed-loop Nash strategy

Coupled algebraic Riccati type equations issued from a Nash strategy with a closed-loop information structure are very difficult to solve. Even if there does not exist an analytic solution of these equations, the literature offers several iterative algorithms to obtain numerical solutions. These algorithms are usually delicate because they imply solving sophisticated equations. This paper provides a simpler algorithm using only one standard algebraic Riccati equation and several Lyapunov equations. For some classical examples considered here, this algorithm leads to a reasonable convergence rate with respect to the algorithms of the literature.