A New Algorithm for Computing the Stabilizing Solution of General Periodic Time-Varying Stochastic Game-Theoretic Riccati Differential Equations

Abstract: We propose a new algorithm for a broad class of periodic time-varying Stochastic Game-Theoretic Riccati Differential Equations arising in Zero-Sum Linear-Quadratic Stochastic Differential Games. The algorithm is constructed via dual-layer matrix-valued functions iteration sequences, which reformulate the original problem into a set of interconnected bilevel subproblems. By sequentially computing the maximal periodic solutions to the Riccati differential equations associated with each subproblem, we derive the stabilizing periodic solutions for the original problem and rigorously prove the algorithm's convergence. Numerical experiments verifies algorithm effectiveness and stability. This study provides a unified numerical framework for solving a wider range of periodic time-varying Stochastic Game-Theoretic Riccati Differential Equations.