Solving Stochastic Linear Quadratic Games in Discrete Time with Two Players Using Exact Line-Double Newton Method

In this paper we consider a two-player stochastic linear quadratic differential games with an infinite horizon in discrete time. We assumed that there is no cooperation between the two players. For the given system, the major problem is solving a pair of stochastic discrete algebraic Riccati equation (SDAR) arising on the given system and its quadratic regulator to find its optimal control form. Thus, we construct a numerical method for solving SDAR using a modified Newton method. This method is modified from its original Newton method and Exact line search method to concise the Newton iteration. We provide a numerical simulation to show the performance of the method.