Iterative solution of algebraic matrix Riccati equations in open loop Nash games

In this note we study a fixed point iteration approach to solve algebraic Riccati equations as they appear in general two player Nash differential games on an infinite time horizon, where the information structure is of open loop type. We obtain conditions for existence and uniqueness of non-negative solutions. The performance of the numerical algorithm is shown in an example. Copyright © 2005 John Wiley & Sons, Ltd.