Abstract
This paper discusses the Nash gables for a class of uncertain weakly coupled large-scale systems. Particu-larly, the infinite horizon stochastic Nash games are addressed by considering uncertainty as state-dependent noise. First, the asymptotic structure for the solutions of the cross-coupled stochastic algebraic Riccati equations (CSAREs) and the condition for the existence of solutions are derived. Second, using such properties, an approx-imate Nash equilibrium strategy that is independent of the coupling parameter ε is established. Moreover, it is shown for the first time that the new strategy achieves O (ε2) approximation. Finally, in order to demonstrate the efficiency of the proposed design method, a numerical example is provided.
