Computing Nash Optimal Strategies for a Two-Player Positive Game

Abstract

We consider a linear quadratic differential game on an infinite time horizon with two types of an information structure.
The game models are considered in both information structures: the open loop design and feedback design. The Newton solver for
computing the stabilizing solution of the associated Nash-Riccati equations has been established. Moreover, a convergent linearized
iterative method depending on a negative constant is introduced for each information structure. The linearized iteration has a linear
convergence rate, however there are cases where the iteration is faster than Newton’s method. Numerical experiments are implemented to explain the computational advantages of the introduced solvers.