Nash Equilibrium Strategy for Weakly Coupled Large - scale Stochastic Systems

This paper discusses the Nash gables for a class of uncertain weakly coupled large-scale systems. Particularly, 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 approximate Nash equilibrium strategy that is independent of the coupling parameter E is established. Moreover, it is shown for the first time that the new strategy achieves O(E2) approximation. Finally, in order to demonstrate the efficiency of the proposed design method, a numerical example is provided.