Recursive computation of stochastic Nash games with state-dependent noise for weakly-coupled large-scale systems

This paper discusses the infinite horizon stochastic Nash games with state-dependent noise. After establishing the asymptotic structure along with the positive semidefiniteness for the solutions of the cross-coupled stochastic algebraic Riccati equation (CSARE), recursive algorithm for solving the CSARE is derived. As a result, it is shown that the proposed algorithm attains linear convergence and the reduced-order computations for sufficiently small parameter epsiv. As another important feature, the high-order approximate strategy that is based on the iterative solutions is proposed. Using such strategy, the degradation of the cost functional is established. Moreover, it is shown that the exponentially mean-square stable is guaranteed. Finally, in order to demonstrate the efficiency of the proposed algorithm, numerical example is given.