Soft-ConstrainedStochasticNashGamesfor WeaklyCoupledLarge-ScaleSystems ?
Abstract
In this paper, we discuss innite-horizon soft-constrained stochastic Nash games involving state-dependent noise in weakly coupled large-scale systems. First, we formulate linear quadratic differential games in which robustness is attained against model uncertainty. It is noteworthy that this is therst time conditions for the existence of robust equilibria have been derived based on the solutions of sets of cross-coupled stochastic algebraic Riccati equations (CSAREs). After establishing an asymptotic structure along with positive deniteness for CSAREs solutions, we derive the formula for Newton's method for solving CSAREs. As another important feature, we propose a high-order approximate Nash strategy based on iterative solutions. Finally, we provide a numerical example to verify the efficiency of the proposed algorithms.